The 23-year-old has recently been linked with a move to Aston Villa and Bolton after impressing since joining Celtic from Maccabi Haifa last summer.
“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.”