Holding midfielder Gareth Barry is approaching the end of his career, and West Brom appear to have identified an ambitious target to come in.
However, Wanyama not only wants to stay at Spurs, but also has no intention of dropping down to the Championship any time soon.
That's no great surprise given that Liverpool and Manchester United were reportedly keen on Wanyama in 2018, and a £40million fee was mentioned by the Daily Mail.
The Kenyan international has endured a miserable 12 months, slipping down the Spurs pecking order despite his close relationship with Pochettino.
The pair worked together at Southampton before reuniting with Spurs in 2016, and Wanyama enjoyed a superb first season as he became a star for Tottenham.
Now though, injuries have taken their toll on Wanyama, and even if West Brom can't land him, it wouldn't be a surprise to see the powerful anchor man move on this month.
The Kenyan midfielder has only started one Premier League game this season, which has been punctuated by knee issues, and is among the four players - including Mousa Dembele, Georges-Kevin Nkoudou and Vincent Janssen, who could be offloaded by Mauricio Pochettino in the next window.
The Baggies, third in the Championship table after 25 rounds of fixtures, want a top-quality midfielder to help propel them back into the Premier League after their relegation last season.
Wanyama has only made a handful of appearances this season since he picked a recurring injury in a match against Barcelona in Spurs’ tour of the United States.