Last season's player of the year has not started a game for the Reds in the current campaign with summer signing Rune Pedersen having been preferred in goal.
Forest have yet to confirm or deny the story which claims that Gerrard is unhappy at playing second fiddle to Pedersen.
The former Everton and Oldham man was linked with a move to join former boss Joe Royle at Ipswich during pre-season.