The 34-year-old has had reconstructive facial surgery after a freak collision with his own goalkeeper in a reserve game on November 28 and will undergo further procedures in 2018.
A report by Sky Sports News published on Tuesday claimed that Yates will not have his contract renewed when it runs out on December 31, but that the Valiants will continue to pay the player's ongoing medical bills.
Vale chief executive Colin Garlick, however, has responded by claiming that it would not be right to discuss Yates's contract situation in the media rather than directly to the player.
"Anything that will be discussed will be discussed with Adam first," Garlick told the Stoke Sentinel.
"The only conversation I have had with him has been relative to his welfare and how he is. So, at the moment I haven't had any discussions with him about his contract."
Yates signed for Vale on a free transfer from Morecambe in 2009 and has made more than 200 appearances for the Staffordshire-based club.