A spokesman for the Abu Dhabi owned club said the 26-year-old was expected to join City for training later on Wednesday once the deal had been finalised.
Ireland international Shay Given, the club's regular goalkeeper, was ruled out for the season after dislocating his shoulder in a 0-0 draw at Arsenal at the weekend.
The club's reserve keeper Stuart Taylor is recovering from knee surgery which left only 23-year-old Gunnar Nielsen, who stood in on Saturday as the first player from the Faroe Islands to appear in the Premier League.
City also have Joe Hart on loan to Birmingham City but said they had failed to reach an agreement to recall him after talks on Tuesday.
Fulop is used to playing on loan - having had stints at Chesterfield, Coventry and Sunderland while on Tottenham Hotspur's books and then joining Leicester and Stoke from Sunderland.
The Hungarian is expected to play against Aston Villa at home on Saturday. City have three games remaining and are sixth in the league, a point behind fourth-placed Tottenham and Villa and one ahead of Liverpool.
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