The Frenchman is also reportedly wanted by Arsenal and Manchester United.
Tolisso has lost his significance at Bayern, who are looking to sell him ahead of the new season.
The French midfielder moved to Allianz Arena from Lyon in 2017 with high expectations but failed to live up to it due to a string of injuries.
As the report states, The Bavarians are open to selling Tolisso for a fee as low as £10m, with his current deal expiring next summer.
Manchester United and Arsenal could provide competition to Spurs as the Premier League duo is also keeping tabs on the French man’s situation at Bayern.
The Gunners are in the market for new midfielders and see Tolisso as a viable option, whereas Man Utd have also been linked with a handful of midfielders other than the Frenchman.
Spurs have already added Bryan Gill, Pierluigi Gollini and Cristian Romero to the squad in what is turning out to be a productive transfer window.
Tolisso could be a great addition to the North Londoners, considering his cheap transfer fee.
Furthermore, the French man is only 27 and can revive his career at Spurs, and his all-around ability can be of great use to Nuno Santo.