Baines and Naismith are struggling with hamstring injuries, while midfield duo Barry and Pienaar have ankle and knee problems respectively.
Naismith was added to Everton's injury list when he had to be withdrawn late on in Saturday's 2-1 Premier League victory over West Ham.
All four players will miss Thursday's UEFA Europa League clash at Wolfsburg and manager Roberto Martinez is unsure if they will feature at White Hart Lane.
The Spaniard said on Wednesday: "It is too early to tell which players may or may not be back for the weekend, but all have a small chance for the weekend.
"Steven Naismith has a soft tissue problem, but we don't think it is serious. He has a 50-50 chance for the weekend."
Arouna Kone could make his long-awaited return to first-team action in Germany after he flew out with the squad on the eve of the Group H encounter.
The Ivorian striker was an unused substitute in the win over Sam Allardyce's side and has not played for the Merseyside club since sustaining a serious knee injury last October.
Martinez is delighted to see the former Wigan Athletic man fully fit as Everton go in search of the point they need to progress in the Europa League.
"We had really good news on Arouna," he said. "He participated in an Under-21s game yesterday and came through really well for 45 minutes.
"He is going to be part of the squad tomorrow and that is fantastic news. We've been really clear with the individual programme we gave him and the Under-21s game fitted really well with that.
"I saw him so free and mobile that I think he is now ready to be involved with the first team."
