As the sun rises on the 2015 NBA Draft, the Celtics are discovering that the price for a move into the Top 10 may be prohibitive.

“Teams are falling in love with their picks,” a league source said yesterday.

Though Danny Ainge has plenty of time to entice someone into a move, the Celtics have drawn a very strong conclusion about this year’s draft order. If they can’t move into the Top 10 tonight, they have determined that it makes better sense to stay at pick Nos. 16 and 28.

If only the talent at that level was more stirring.

“I’m trying to fall in love,” Ainge said earlier this week.

With that in mind, don’t fall in love with this mock draft. History says that it will break your heart, or make you laugh.

1. MINNESOTA (Karl-Anthony Towns, C, Kentucky freshman) – They will probably go on a Cleveland or Philly-like run in terms of rookie of the year talent – last year with a great future scorer in Andrew Wiggins, this time a center with everything, including offensive polish, huge defensive upside, size and strength. Towns may be the only franchise player in this draft.

2. LA LAKERS (Jahlil Okafor, C, Duke freshman) – With the exception of Magic Johnson, each great Lakers era has been identified by a marquee big man. Okafor comes equipped with the kind of old school post offense that looks at home in purple and gold.

3. PHILADELPHIA (DeAngelo Russell, PG, Ohio State freshman) – They’ve traded away two elite point guard talents (Jrue Holiday, Michael Carter Williams) in the last two years, and Russell should be better than either. The Joel Embiid setback aside, this has become a point guard league. Russell could be one of the best. Then again, perhaps GM Sam Hinkie continues along his bizarre path.

4. NEW YORK (Kristaps Porzingis, PF, Latvia) – Phil Jackson is determined to make a splash in his first draft as a GM, while also finding a triangle-friendly talent. He wants Russell, who should be gone. He reportedly likes Trey Lyles, Frank Kaminsky and Willie Cauley-Stein, but can trade down for all of them, and may do just that. But if this remains the pick, he’ll leave Knicks nation howling, and ignore immediate help in favor of this uber-talented project.

5. ORLANDO (Willie Cauley-Stein, C, Kentucky junior) – The Magic most desire a power forward to put next to the talented Nik Vucevic. We have them missing out on Porzingis. Though Cauley-Stein is more of a center, he has enough athleticism to cover wings and bigs alike. Offense is a problem, though he can blossom rolling to the rim off Elfrid Payton lobs.

6. SACRAMENTO (Emmanuel Mudiay, PG, Congo) – He chose China over college, injured his ankle, and barely played. Mudiay’s pre-draft workouts reportedly weren’t especially good, either. Thus this brief slide. He may not have the polish and overall flair of Russell, but he’s a better athlete, more explosive with great size. The Kings, a year after letting Isaiah Thomas go, are still in a point guard quandary.

7. DENVER (Mario Hezonja, SG, Croatia) – Perhaps the best shooter in the draft, Hezonja also has what some have described as a confidence overload. A potential star for Denver, which is once again starting from scratch.

8. DETROIT (Justise Winslow, SF, Duke freshman) – Though Winslow’s shooting has been called into question, he’s a another with future star potential. He has an NBA-ready body. Though his erratic shot may create spacing problems, he’s too good to pass up here.

9. CHARLOTTE (Devin Booker, SG, Kentucky freshman) – Possibly the equal of Hezonja or better as a shooter, and lord knows the Hornets need shooting. Their lack of 3-point shooting made Al Jefferson’s life very rough last season.

10. MIAMI (Stanley Johnson, SF, Arizona freshman) – Amid angst over the futures of Dwyane Wade and Luol Deng, the Heat can’t predict the future with this pick. They end up with the best player remaining on the board, one of the best defenders in the draft, and someone who has dropped this low because his jump shot needs lots of work.

11. INDIANA (Trey Lyles, PF, Kentucky freshman) – The slow combination of an aging David West and the wooden Roy Hibbert cried for a young shot of energy last season. No one is quite sure what Lyles does exceptionally well, but many feel his true value was obscured by Kentucky’s platoon system. There’s a need for him here. West will also be a free agent.

12. UTAH (Frank Kaminsky, C, Wisconsin senior) – The Jazz just can’t seem to get their front court in order since allowing Paul Millsap to get away. Their power forward of the future, Derrick Favors, would benefit greatly from a skilled floor-spacing big. Those are two things Kaminsky can do exceptionally well.

13. PHOENIX (Myles Turner, C, Texas freshman) – Turner has one of the most unpredictable trajectories in the draft. He could go anywhere from here to the low teens, though he refused workouts with teams in that range, including the Celtics. Phoenix needs a big man with skill. The only question about Turner is athleticism. He has mobility issues.

14. OKLAHOMA CITY (Cameron Payne, PG, Murray State sophomore) – Other point guards (especially Reggie Jackson) have been uncomfortable sharing the floor with Russell Westbrook. But this scoring point with a high basketball IQ offers a logical option to try again.

15. ATLANTA (Sam Dekker, SF, Wisconsin junior, 6-foot-9, 220) – The impending free agencies of Millsap and DeMarre Carroll loom big here, with the Hawks more likely to overpay the former instead of the latter. If so, they’re going to need a versatile defender with skill and proven, albeit streaky 3-point range. That describes Dekker.

16. CELTICS (Bobby Portis, PF, Arkansas sophomore) – If stuck here, the Celtics like a wide range of players, from defense-oriented small forwards (Justin Anderson and Rondae Hollis-Jefferson) to athletic power forwards (Montrezl Harrell and Kevon Looney). Kelly Oubre will give them pause because of his scoring potential. But Portis is the most offensively gifted big left on the board, and satisfies a huge Celtic deficiency on the glass. He’s relentless in that department.

17. MILWAUKEE (Kevon Looney, PF, UCLA freshman) – Though he has a hip issue that may require surgery, Looney is emerging as a swing forward who can score. He also has a high motor. The Bucks, after trading Ersan Ilyasova to Detroit, need energetic offense around the basket.

18. HOUSTON (Jerian Grant, PG, Notre Dame senior) – The Rockets have had a point guard issue for several years now, especially exposed after losing Patrick Beverley for the playoffs. Grant may not have as much upside as younger players, but as evidenced by his role in Notre Dame’s run to the Elite Eight, he’s ready to contribute.

19. WASHINGTON (Montrezl Harrell, PF, Louisville junior) – A player who could easily go to the Celtics at No. 16, Harrell is a physical defender without much in the way of perimeter offense. But the Wizards have plenty to complement him from the perimeter. They’re not going to replace Paul Pierce’s offense in the draft, anyway.

20. TORONTO (Kelly Oubre, SF, Kansas freshman) – Oubre, once considered top 10 material, has drifted despite having as good a combination of offense and defense as anyone this side of Justise Winslow. He’d be a nice youngster to bring along on one of the most intriguing young teams in the East.

21. DALLAS (Tyus Jones, PG, Duke freshman) – He’s shown great leadership in a small sample size in college. The Mavericks, following that painful Rajon Rondo experiment, are still searching for a point guard willing to play Rick Carlisle’s way.

22. CHICAGO (Rondae Hollis-Jefferson, SF, Arizona sophomore) – The Bulls are in a state of flux, with rumors that impending free agent Jimmy Butler was bothered by management’s treatment of the deposed Tom Thibodeau. Hollis-Jefferson won’t contribute offensively, but he defends in Thibodeau’s, er, Chicago’s style.

23. PORTLAND (R.J. Hunter, SG, Georgia State junior) – Hunter has been all over the board thanks to a disappointing junior year and a favorable workout season. He could be a shooter on the level of Hezonja and Booker. The Blazers, who could lose LaMarcus Aldridge and Wesley Matthews to free agency, aren’t going to replace the former this late in the draft. But Hunter offers a chance to replace Matthews’ range.

24. CLEVELAND (Rashad Vaughn, SG, UNLV freshman) – Vaughn has moved up the board with some impressive workouts, and projects as a talented shooter. For a Cavs team reeling from a J.R. Smith hangover, it could be helpful to know there’s a young understudy.

25. MEMPHIS (Justin Anderson, SF, Virginia senior) – The rugged, aggressive Anderson will immediately fit in Memphis. He also projects as a so-called 3-and-D player. Memphis needs shooting.

26. SAN ANTONIO (Guillermo Hernangomez, C, Spain) – The Spurs can stash him in Europe for the next two years. When’s the last time you heard that.

27. LA LAKERS (Delon Wright, PG, Utah senior) – Their big man of the future in place, the Lakers can now address their lack of point guard depth. Wright’s readiness is high.

28. CELTICS (Cedi Osman, SF, Turkey) – They would dearly like to trade out of this pick, but this is also the stage to take a gamble. Osman is an intriguing scorer with above average athleticism. He’s probably the third best international in a weak international year. He suits the Celtics because he can be stashed overseas for a year or two.

29. BROOKLYN (Jarrell Martin, PF, LSU sophomore) – They’re dangling Mason Plumlee as trade bait, and Thaddeus Young has opted out. Martin offers a physical, aggressive style to start filling that hole.

30. GOLDEN STATE (Christian Wood, PF, UNLV freshman) – The NBA champs want to get rid of David Lee. It’s time to bring in a young big man, even if the Warriors don’t always use players like that.