Murray, a two-sport star, was chosen by the A's with the ninth pick of the MLB draft in 2018 and signed a deal in June that included a $4.66 million signing bonus and allowed him to play football for the Sooners for one final season before joining the A's.
Murray, 21, complicated things by leading Oklahoma to a 12-2 record and a spot in the College Football Playoff, winning the Heisman Trophy along the way.
ESPN draft experts Mel Kiper Jr. and Todd McShay have noted that Murray could be a first-round pick, and ESPN's Chris Mortensen reported Wednesday that Murray was getting "first-round feedback" regarding the NFL. Last month, an NFL general manager told ESPN's Adam Schefter: "I really believe he's a first-round pick, a late first, I really do."
Declaring for the NFL draft would not guarantee that Murray would choose football, and the A's would retain his professional rights, even if he tried the NFL first.
If Murray chooses the NFL over baseball, he would have to return his signing bonus, though the A's would not get a compensation pick in the June draft.
The A's were told recently that Murray would not be going back to Oklahoma, sources told ESPN's Jeff Passan. The A's still expect him to report to spring training in mid-February, and the plan is to keep him in major league camp until mid-March, when they leave for Japan to start their season, sources said.
The expectation is to have Murray start his professional career at Oakland's high-A affiliate in Stockton, California, sources said.
Murray's agent, Scott Boras, told ESPN on Wednesday night that his client "has a baseball contract." Boras has been steadfast that Murray will play baseball now that Oklahoma's football season is over.
The A's might consider giving Murray permission to go to the NFL scouting combine, according to the San Francisco Chronicle, citing a source. Major League Baseball would also have to approve Murray's attendance at the combine.
Kingsbury in 2018: I would take Murray with No. 1 pick
Arizona head coach Kliff Kingsbury said in 2018 he'd select Kyler Murray with the first overall pick. The Cardinals hold the top selection in the 2019 draft.
Murray will need to make a decision in the next month. Spring training for the A's opens Feb. 15, and it seems unlikely he would be able to prepare for football's scouting combine at the same time as attending his first major league baseball camp.
Last month, on the eve of the Heisman ceremony, it was clear Murray was torn about which sport he wanted to play.
"I'd like to do both, if possible,'' he said. "But I don't know how possible that is."
The Chronicle reported that one source told the paper Murray is leaning toward football.
After his team lost to Alabama in the College Football Playoff semifinal, Murray was mum about his future.