Spurs decided to part company with the 58-year-old Portuguese after a series of poor results and performances, and Gerrard has been listed by the bookmakers as one of the candidates to replace him.
Former RB Leipzig boss Julian Nagelsmann is the 5/2 favourite to land the role with BetVictor, with Leicester boss Brendan Rodgers next in line at 8/1.
Rafa Benitez and current Wolves manager Nuno Espirito Santo are slight outsiders to replace Mourinho, with both priced at 10/1.
Gerrard is named at 12/1 along with Carlo Ancelotti and Massimiliano Allegri.
How likely would a move to Spurs be?
While he would obviously be flattered by any approach from Tottenham, Gerrard is extremely content at Rangers.
Having already won the league, the Ibrox club are now favourites for the Scottish Cup and will play Champions League football next season.
With Liverpool always touted has his next destination due to his links with the Merseyside club, Tottenham could be seen as a potential stepping stone. However, Nagelsmann – or even former Celtic boss Rodgers – seem far more suitable candidates at this stage.