The Israel midfielder was one of Neil Lennon's most impressive performers in his debut season at the club despite missing most of the first half of the campaign with a groin injury.
Kayal has been linked with English clubs, and Bolton manager Owen Coyle has reportedly been lining up a bid.
The 23-year-old has three years left on his Celtic contract but wants an improved deal if the club decide to hold on to him.
Kayal said: "I enjoy it at Celtic and I want to stay, but who knows what will happen in the next few weeks?
"These discussions are nothing to do with me. It's a question for the people who are in charge and it will depend on them.
"I like Celtic, I like the fans, I like the manager and I would be very happy to keep playing for the club. But they must treat me at the level I deserve."
Certainly Kayal, who broke his wrist in the 3-2 defeat at Inverness last month that spelled the end of Celtic's Clydesdale Bank Premier League title hopes, does appear determined to lift silverware at Parkhead.
The former Maccabi Haifa player, who missed the Scottish Cup final win over Motherwell, added: "It is my wish to enjoy at least one more full season at Celtic and to give the fans and, especially, Neil Lennon my best form because we can be champions."