The Israeli international impressed during his debut season with Celtic and his form has alerted both the Trotters and Aston Villa, but the player says he is going nowhere.
The 23-year-old has confirmed that negotiations have begun over a new contract at Parkhead and he is hopeful of putting pen to paper.
“Celtic spoke with me this week and we have opened negotiations on a new contract,” Kayal told the Daily Record.
“Last season I received quite a few offers but I told all the clubs I want to be at Celtic. It’s very important to me that myself and Celtic are satisfied with my new deal.
“I have a new agent now and I expect him to tie up my new deal. It’s nice to get other proposals but it is most important for me to stay.”
Wanderers boss Owen Coyle is looking at a number of midfielders but it looks as though he will have to turn his attentions elsewhere now that Kayal has ruled out a move.
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.