The Kenyan midfielder was reportedly in London on Monday to complete a medical ahead of an expected transfer, according to Sky News.
Spurs boss Mauricio Pochettino is a big fan of Wanyama, who he signed from Celtic when manager of Southampton.
Pochettino tried to sign the Kenyan last summer, but the move was blocked, reportedly leaving the player unhappy.
Now, with just one year left on Wanyama's contract, Southampton are looking to get their money back for a player who cost them £12.5-million when he made the move south from Scotland.
Spurs are said to be keen to sign another midfielder ahead of a Champions League campaign after finishing third in the Premier League last season.