At first, it was possible. Now, it looks as if it is probable the Giants take running back Saquon Barkley with the No. 2 pick in the draft. Is there another, stronger, word to describe this unfolding scenario?

“It just feels to me, like it’s inevitable that Saquon Barkley is going to be a New York Giant,’’ ESPN draft analyst Todd McShay said Wednesday on a conference call.

McShay said he is basing this not only on the regard he has for Barkley.

“I’ve heard really strongly that there are important people in that building who believe in Saquon Barkley, the player, that’s what they want to be,’’ McShay said. “The Giants want to be a run-first, physical football team, and Saquon can basically be the face of that franchise moving forward for several years.’’

This would be a departure for the Giants, as they have structured their offense for more than a decade around Eli Manning’s passing setting up the running game. With Odell Beckham Jr., Sterling Shepard and tight end Evan Engram, there are targets on the outside to fuel a passing game.

This is a new regime, though. General Manager Dave Gettleman favors “hog-mollies’’ on his offensive line and is a believer that the bigger, stronger team usually wins. New head coach Pat Shurmur has a history of directing balanced offenses that often use the run to set up the pass. Plus, Shurmur loves to throw the ball to running backs. So, Barkley certainly makes sense as the pick.

“He can be the back that they’ve had in years past,’’ McShay said. “If you spend 10 minutes with Saquon, you understand that he’s going to be the face of a franchise. He’s so likeable, so easy to get along with. He’s a great, genuine young man who loves the game and is going to give you everything that he’s got every week.’’

This is an extremely deep draft class for running backs, and the Giants could wait until the second or third round to add one. But they would not be getting a Saquon Barkley, who fits Gettleman’s criteria for the No. 2 pick: A player you can envision one day being a Hall of Famer and a player worthy of the No. 2 pick not only this year, but every year.

“There are a lot of good running backs in this class, but this guy’s different,” McShay said. “If you’re committed to the running game, and that’s what you want to be as an organization, then it makes sense to take Barkley. The Giants want to be a run-first team. That’s what I’m told their emphasis is. If that’s the case, Barkley makes all the sense in the world.’’

Barkley is the best running back to come out of a draft since Adrian Peterson, according to Gil Brandt, the former longtime Cowboys executive and now an analyst for SiriusXM NFL Radio.

“I think he’s a special player,’’ Brandt said. “I think Barkley is going to be a future star in this league.’’