Hart has lost his place in the Manchester City side after a series of high-profile mistakes, raising questions over his position in the national team.
Cottee told the Mirror: "I don't think Joe should play in these two games anyway.
"We know what he can do, we know how good he is.
"He is not in the team at City at the moment, and we understand that, but I think it is time for Fraser Forster to be given a chance.
"He has done very well at Celtic and is playing Champions League football."
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