The 21 year was one of the Scottish sides stand out players on route to the last sixteen of the Champions League last season, drawing interest from a whole host of English clubs.
Sources in Scotland claim that Celtic would be willing to sell the Kenyan international, though they are demanding a fee in excess of £10 million.
Wanyama moved to Celtic Park from Belgian side Beerschot two years ago, and has since scored ten goals in sixty-one Scottish Premier League appearances.
Southampton and Cardiff both have budgets to enable them to make a move, and are ready to test Celtic’s resolve, while Turkish giants Galatasary also have an active interest.
Stoke City, Newcastle United and Liverpool are also said to be monitoring the situation, though previous interest from Arsenal and Premier League champions Manchester United has quietened.