The midfielder hit the headlines this week with an attack on Rangers skipper Lee McCulloch and a blast at the standard of Scottish football.
Kayal has just one season left on his Hoops contract and Hay wouldn't be surprised to see him shipped out as part of Neil Lennon's summer rebuilding work.
He said: "I think there is a chance he will leave.
"He has been getting less and less first-team starts and Neil is not short of options in the middle of the park.
"Scott Brown has been excellent again this year, Charlie Mulgrew is there, Stefan Johansen has done well since coming in in January and Liam Henderson has come through in the last couple of weeks as well.
"That might all have a bearing on it and you might well see Kayal move on.
"You don't like to say a player won't be missed. But, what I would say, is that Celtic are well covered in that position."
Kayal made an instant impact at Parkhead when he joined the Hoops from Maccabi Haifa in 2010.
The Israeli midfielder was later linked with a series of multi-million pound moves, with Manchester United and Liverpool reportedly monitoring him.
He claimed the ankle damage inflicted by McCulloch in an Old Firm clash at Parkhead halted his progress.
However, Hay reckons his frustrations have got the better of him following his outburst this week.
The former Celtic manager said: "That injury, and one or two others, held him back and he was never the same, strong midfield player that he was early doors. That is obviously the way he feels.
"It happened so long ago but it was a harsh challenge.
"It is probably sourness from him now because his career hasn't developed the way he thought it would have and might have done.
"That injury set him back and he never imposed himself the way he did prior to it.
"I am sure that will be a frustration for Beram and he has reacted this week.
"He was progressing well but, after that injury, he did not devleop into the player we thought he would do.
"If he had been playing regularly, he wouldn't have made the comments he did about Scottish football.
"It is down to frustration that he has not done what he thought he would do at Celtic."