Spurs have already strengthened their attack with the signing of Mohammed Kudus from West Ham United, but Grealish could be the next addition to their squad.
The 29-year-old England international has been linked with a move to Everton, but Tottenham's offer of Champions League football may prove to be a deciding factor in his decision.
Grealish had a successful season with Manchester City, scoring eight goal involvements in 32 appearances, but his high wages may make him a difficult signing for any club.
Former England international Gareth Barry has praised the idea of Grealish joining Everton, saying it would be a great move for the player as he would be able to play regular football and potentially regain his place in the England squad.
The competition for Grealish's signature is fierce, with West Ham and Napoli also interested in signing him. However, Tottenham's early enquiries suggest that they are serious about bringing him to the club.
Grealish must now make a decision about his future, and it remains to be seen whether he will choose to join Tottenham or Everton.