Wanyama was injured in training and missed Spurs' last league match against Burnley. He withdrew from Kenya's squad for their recent friendly international with Mozambique and Tottenham said on Thursday he would be out for a "few weeks".
Tottenham manager Mauricio Pochettino is also unlikely to risk new signing Serge Aurier against Everton, as the Ivory Coast international will only return to the club from international duty later on Thursday.
"We need to assess (Aurier) because he will arrive this afternoon in a few hours... because he played Tuesday and travelled today to France, Paris, and now he's travelled from France to London," Pochettino told a news conference.
"We need to see how he is. But you can imagine for him it will be very tough to play... We need to assess him today and tomorrow."
Pochettino also said defender Toby Alderweireld was happy at the club and ruled out the Belgium international moving away in January after the player's agent called on Tottenham earlier this week to offer his client improved terms.
"(Alderweireld) was talking with me in my office this morning and he's so happy, he wants to make it clear he is fully committed with the club," the manager said.
"He's happy with his contract, two years plus one. It's not an issue. I recognise some rumours in the last few days. But he is so relaxed, so calm. His idea is to try to play here... there's no reason to move."
The Argentine urged his players to bounce back strongly from the disappointment of drawing 1-1 with Burnley in their last league match.
"Always our ambition is to win," Pochettino said. "It's true that in the last game at Wembley we were disappointed with the result. Now we have an opportunity to get three points.
"We have a lot of respect for Everton. They have a great manager and great players. They signed a lot of players during the transfer window. It's a new Everton but it's still the same philosophy and course it will be a very tough game."
(Reporting by Ken Ferris in London; Writing by Simon Jennings in Bengaluru, editing by Pritha Sarkar)
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