Midfielder Sean has been sidelined for a month with tendonitis of the kneecap but has trained this week and could play some part at Goodison Park.
Thimothee Atouba could also return after recovering from the leg injury he sustained against Chelsea.
However, Fredi has been ruled out with the hamstring strain that forced him off early against Manchester United last weekend.
Head Coach Jacques Santini reported this afternoon: "We have good news on Atouba and Sean Davis but Michael Carrick is not fit and Kanoute is also injured for this game.
"Sean hasn't played for three weeks but it's possible he'll be in the 16 players and possibly a substitute but I would prefer to wait for our final training session on Friday before I make my decision.
"If Sean is in the squad it's possible he won't begin the game because he hasn't had enough training sessions. It's similar to when Robbie Keane and Simon Davies came back from injury and were substitute to start with.
"Fredi has had some individual training sessions but it too early for him to play on Saturday."
Sean Davis looks set to return to the squad for Saturday's trip to Everton but Fredi Kanoute is out.