Right-back Walker turned his ankle at home on Monday, meaning boss Mauricio Pochettino could be without both of his first-choice full-backs, with Danny Rose still sidelined.
Former Southampton star Wanyama is also a doubt as he struggles to shake off a knock picked up in the 6-0 FA Cup quarter-final win over Millwall.
Should the Kenyan miss out then Pochettino may be forced to change his formation, with Eric Dier, who has been part of a three-man defence for Spurs in recent weeks, the likely choice to start in Wanyama's place in midfield.
Erik Lamela remains on the sidelines with a hip injury while Harry Kane misses out for the first time since he damaged ankle ligaments last weekend.
Heung-Min Son and Vincent Janssen will battle it out to start up front in Kane's absence and Pochettino claims to be happy to have the duo amongst his squad, believing they can fill in for Spurs' top scorer.
Pochettino said: "What we can do now is find a solution. We have many players that can cope with the pressure.
"We can cope. It is a similar situation to earlier in the season. We lost Harry Kane for seven or eight weeks and one of the best performances was without him against Manchester City, when we won 2-0.
"We showed in 80 minutes against Millwall [without Kane] that we scored six goals. Sonny scored a hat-trick, Vincent Janssen scored, and Dele Alli. We are very confident in our players. We must not make excuses but try to score goals and win games."