The keeper was named in Roy Hodgson's England squad for the friendly with Denmark next week and will battle it out with John Ruddy and Ben Foster for a seat on the plane to Brazil.
Hay told SportTimes: "If Fraser does go to the World Cup, it could convince him that he doesn't need to leave Celtic to further his England ambitions.
"I think he is enjoying life at Celtic and he has never made any noises that he wants to leave the club.
"Celtic have given him the chance to play in the Champions League and now at international level as well.
"The time may come where an offer comes in that suits all parties and Fraser does leave but the fact that he is getting international call-ups while at Celtic is a positive."
The keeper last weekend set a new Scottish shut-out record before Celtic crashed 2-1 to Aberdeen in midweek.