HITC Sport understands Tottenham Hotspur are keen to tie up deal.
The 23-year-old Kenyan midfielder has become one of the Saints' leading performers since joining from Celtic threeyears ago and he has just one year left on his current deal.
Wanyama has told Southampton not to even offer him a new deal as he will not entertain the prospect of extending his stay at St Mary's as he feels the time is right to make the move.
HITC Sport can reveal that Tottenham chief Daniel Levy has made contact with Southampton about the player, who manager Mauricio Pochettino is convinced would slot into his midfield having previously working with him on the South Coast.
Southampton know they are now left in a situation that this summer is the final time they can get good money from their Kenyan star, as he can sign a pre-contract with another club come January.
Ronald Koeman is loath to lose Wanyama but has accepted that he is highly unlikely to be part of his squad next season.