Forster joined Celtic on a permanent basis from Newcastle 12 months ago after enjoying two seasons on loan at Parkhead.
He still has three years left on his contract, but is a target for Benfica after impressing against the Portuguese club in the UEFA Champions League last season.
However, Celtic boss Neil Lennon has regularly stated his intention to keep hold of Forster and the Scottish champions have no wish to sell the 25-year-old.
The England hopeful will again be looking to catch the eye in the Champions League, with Celtic facing Kazakhstan side Shakhter Karagandy in the first leg of their play-off tie on Tuesday.
Earlier this summer, Forster was linked with a move to Sunderland to replace Simon Mignolet, who was sold to Liverpool.