The Scottish Sun claim the former Celtic linchpin will accept a five-year deal, worth £65,000-a-week.
Wanyama has struggled to get regular game time in north London after suffering a succession of injuries following his move from Southampton three years ago.
And the club-record signing of Tanguy Ndombele, coupled with the emergence of Harry Winks and Oliver Skipp, means Pochettino believes the 28-year-old is now surplus to requirements.
“It’s all about performance,” he said after the 1-0 defeat to Newcastle on Sunday. “Football is for today and tomorrow, not yesterday. You need always to show that you are there and deserve (to be there).
“In the case of Victor, he suffered an injury and another player stepped up and took his place. We are in a team, we are not a charity.
“I am making clear the answer is not about Victor, but we are not a charity – it is about performance and the coaching staff have a lot of different options to play different players.
“I am the coach, I need to take the decision and hope it will be right. Victor is a very important player and, for different circumstances, went backwards.
“That is the evolution of football and things like that happen naturally at all clubs.”
Wanyama is yet to make an appearance for Spurs this season, featuring just 22 times in the previous campaign as Poch’s threadbare squad reached the Champions League final.
He has made 93 appearances in total for Spurs, scoring seven times across a three-year period dogged by persistent knee injuries.