Forster has been in fine form for the Hoops this season, keeping 12 straight clean sheets in the league, prompting suggestions that he may move on in the summer.
Sky Sports pundit Walker, who played for Celtic in the late 1980s and in the '90s, believes the day will come when Forster follows the footsteps of Hull City's Allan McGregor (formerly of Rangers), Cardiff City's David Marshall (previously with Celtic), Newcastle United's Tim Krul (loan with Falkirk) and Crystal Palace's Julian Speroni (from Dundee).
"I'm sure Fraser will probably move on from Celtic pretty soon and I have no doubt he will do a good job at the top level down there."
Of Forster's hopes of making England's World Cup squad, Walker added: "He has great ability and I know there is talk of whether he should be in the England set up.
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