Stokes has been on the books of Scottish Premiership giants since 2010, but he is struggling for playing time at the moment and has fallen down the pecking order.
“The 27-year-old hitman still has one more year left on his contract but it could be that he tries to force a move in the January transfer window,” former Celtic midfielder Hay wrote in The Glasgow Evening Times.
“It seems detrimental to both parties to have him around the club if there is no chance of his getting a game or into the squad.
“His days at Parkhead would seem to be numbered and with the addition of Carlton Cole last month then you would have to wonder where he would fit back in.”
Celtic manager Ronny Deila has Leigh Griffiths, Nadir Ciftci and Carlton Cole to call upon in attack, which means that Stokes, who can also play out wide, is currently the fourth-choice striker at Celtic Park.
The Republic of Ireland international will certainly want to play, and it would make sense if he decides to leave the Bhoys in the January transfer window.
The Hoops would not miss the former Sunderland and Hibernian striker if he does leave.
Celtic are at the top of the Scottish Premiership table at the moment with 35 points from 14 matches.
The Glasgow outfit are six points clear of second-place Hearts and are on course to winning the Scottish Premiership title yet again.