The 25-year old Hoops keeper is a reported target for a number of clubs around Europe such as Barcelona, Real Madrid and Juventus which has him linked with a possible Celtic Park departure this summer.
However, Woods feels that Forster, who is in the running for Roy Hodgson's Three Lions roster for Brazil 2014, is every chance of staying put at Parkhead if he lands a spot in the 23-man squad for the FIFA tournament.
"There have been some admiring glances from all over Europe and that's credit to him," Woods told The Sun of the former Newcastle United gloveman.
"Fraser is contracted here for another couple of years. He's very happy. If we can get him to the World Cup as a Celtic player, there is no reason for him to leave."
Forster is one of four keepers in the Three Lions squad for Wednesday night's friendly with Denmark, joining number one Joe Hart (Manchester City), John Ruddy (Norwich City) and Ben Foster (West Bromwich Albion).
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