The Daily Mail reports that all four clubs hold genuine interest in the England international, whose creative quality and intensity in the press have attracted consistent attention from top-flight rivals.
Manchester United, Spurs, Chelsea and Aston Villa, however, currently have players operating in similar positions, limiting the urgency of a formal approach.
Nottingham Forest's position is firm. Gibbs-White signed a new contract at the City Ground twelve months ago — shortly after Tottenham triggered a release clause to make a formal bid — and the club have no financial pressure to sell a player they regard as central to their ambitions in the coming season.
Whether Gibbs-White's own outlook shifts over the course of next season's Champions League campaign — which will expose him to the highest level of European competition for the first time — is likely to be the determining factor in whether interest from United or any of the other clubs eventually becomes something more than admiration.