Reports suggested the two clubs were some way apart in their valuations of the midfielder but it now appears they have come to an agreement for the 28-year-old.
The fee reportedly taking the midfielder to Belgium is believed to be an up front cost of £9.1million with an extra £4.6million should Brugge qualify for the Champions League, reports Soccer Link.
There are just a ‘few details’ to iron out before the deal is made official.
Wanyama started just twelve times last season, with Harry Winks, Moussa Sissoko and Eric Dier the preferred options in the deep lying midfield role.
The arrival of Tangy Ndombele from Lyon for £53.7million this summer has meant first team appearances for Wanyama will be even harder to come by.
The Kenyan international joined Southampton from Celtic for £13million and then moved to White Hart Lane in 2016 for the same fee.
Wanyama played in Belgium with Beerschot AC for three seasons before moving to Scotland.