The midfielder has been excellent for Ronald Koeman's side this season.
Southampton are hopeful that they may be able to convince Victor Wanyama to ignore speculation linking him with a move away from St Mary's, and instead commit his long-term future to the south coast club, according to the Southern Daily Echo.
The 24-year-old tried to bag a move to Tottenham during the summer (via Echo), and remains linked with a reunion with former boss Mauricio Pochettino at White Hart Lane, while Arsenal's hunt to find support for Francis Coquelin in the holding midfielder role has led to them being linked with the Kenyan also, the Daily Echo reports.
However, Saints are hopeful that with 18 months left on his current deal, they can convince Wanyama to agree a new five-year contract, the Echo adds.
With the former Celtic man remaining an integral part of Ronald Koeman's side this season, agreeing a new deal could be critical to the team's chances of progressing further. His ability to break up the play has made it much easier for the club to get over losing Morgan Schneiderlin to Manchester United during the previous window.
Without a long-term commitment from the player however, the club may find that they have to sell the stalwart in the coming months should it become obvious that he still wishes to leave, or risk losing him for nothing next summer.