Buster Olney says securing Twins pitcher Jaime Garcia won't preclude New York from pursuing Oakland's Sonny Gray, who has been scratched from Monday's start. (0:31)

The Oakland Athletics and New York Yankees continue to discuss a potential trade for right-hander Sonny Gray, with both sides making concessions but no agreement reached yet, sources told ESPN.

Gray, one of the marquee names being shopped, was scheduled to pitch Sunday for Oakland but had that start pushed back to Monday night -- hours after the 4 p.m. non-waiver trade deadline.

Earlier Saturday, a source told ESPN that Athletics executive vice president Billy Beane was ready to "walk away'' and try again this offseason if he can't land the package he wants for Gray.

The source said that Yankees outfielder Clint Frazier and prized infield prospect Gleyber Torres -- two names mentioned as targets of Oakland -- are not in play in trade discussions. The Yankees, the source said, made it clear from the outset that Frazier and Torres were off-limits, so the Athletics turned their attention to other players in New York's minor league system.

While Torres is considered a rising star and Frazier has hit four home runs and slugged .537 in 21 games since his arrival in New York, the Yankees have several other highly regarded prospects in a farm system ranked fifth in the game by ESPN's Keith Law. The list includes pitchers Chance Adams and Justus Sheffield, infielder Jorge Mateo and outfielders Dustin Fowler and Estevan Florial.

The Yankees are also believed to be reluctant to part with pitcher James Kaprielian, a 2015 first-round pick who underwent Tommy John surgery in April.

Along with Texas Rangers right-hander Yu Darvish, the 27-year-old Gray is one of the top names being shopped ahead of Monday's deadline. He's 44-36 with a 3.42 ERA and one All-Star appearance over parts of five seasons with Oakland.

Although several clubs have expressed concern about Gray's injury history, the fact that he isn't eligible for free agency until after the 2019 season has been a major selling point for the A's in trade talks.

The Los Angeles Dodgers, Houston Astros, Milwaukee Brewers, Atlanta Braves and Seattle Mariners are among other clubs that have expressed interest in Gray.

Sources said the Yankees are prepared to go in a different direction if they can't land Gray. St. Louis Cardinals right-hander Lance Lynn and Miami Marlins starter Dan Straily have been mentioned as potential alternatives for New York.

The Yankees have been linked to both Gray and Oakland first baseman Yonder Alonso in a package deal, but a source said New York's main objective is acquiring a starter. Chase Headley has a slash line of .317/.364/.415 in July, and his production has reduced the need for a first-base upgrade in the Bronx.