The central midfielder has not played for Mauricio Pochettino's side this season.
He is down the pecking order and given his age of 28, Spurs would not mind cashing in on him.
Sky Sports says £12 million deal with Brugge is near agreement.
Any transfer must be done by September 2, as it is the deadline for the closing of the European transfer window.
Wanyama has been with Spurs since 2016, playing 93 times for the club.