Jon Morosi of the MLB Network reported the update Friday but noted there's no "present momentum" toward finalizing a deal.
Gray is coming off a down year with the Yanks. He posted a 4.90 ERA and 1.50 WHIP across 30 appearances (23 starts). He was demoted to the bullpen in early August amid the struggles.
New York general manager Brian Cashman admitted in October the front office would look to move the veteran starter during the offseason.
"It hasn't worked out thus far," Cashman told reporters. "I think he's extremely talented. We'll enter the winter, unfortunately, open-minded to a relocation. To maximize his abilities, it would be more likely best [for him to be] somewhere else."
Perhaps a return to Oakland could get Gray's career back on track.
The 29-year-old Tennessee native compiled a 3.42 ERA and 1.20 WHIP with 607 strikeouts in 705 innings during his first stint with the A's. That includes a terrific 2015 campaign when he ranked third in the American League with a 2.73 ERA and earned his only All-Star Game selection.
It would be a low-risk acquisition for the Athletics. Gray is set to enter his final year of arbitration in 2019 and can become an unrestricted free agent after next season, so if he doesn't bounce back, the team can let him hit the open market without a major financial investment.
Meanwhile, the Yankees' asking price shouldn't be too high given Cashman's public comments about looking to move the starter.
If Gray does wind up back in Oakland, he'd likely compete with Chris Bassitt and Andrew Triggs for a spot in the A's rotation next season. It's a battle he would likely win, giving him a chance to rebuild his value before a potential foray into free agency.