The England left-back suffered a broken toe in the thrilling 3-3 Merseyside derby against Liverpool last weekend and will be out for up to six weeks.
Baines' absence leaves a big void for manager Roberto Martinez to fill and the Spaniard revealed he will decide who will replace the former Wigan Athletic man after running the rule over potential candidates in training this week.
Everton are unbeaten at home this season, but they need to start turning draws into wins if they are to qualify for Europe as they have had to settle for a point in half of their 12 games so far this season.
Martinez's charges are unbeaten in five games and will be boosted by the inclusion of defender Antonlin Alcaraz in the squad after he came through 45 minutes of a behind-closed-doors game against Sheffield Wednesday this week.
The Paraguay international has not played for the Merseyside outfit since his move from Wigan in July due to a hamstring injury, but he could make his debut against Stoke.
Striker Arouna Kone and Darron Gibson are long-term absentees due to knee injuries.
Nikica Jelavic has been linked with a move away from Goodison Park, but Martinez insisted the striker still has a part to play at the club.
"It (speculation) doesn't surprise me because obviously Nikica Jelavic is a terrific player to have, he's a goalscorer and you don't get them easily in the game." he said.
"From our point of view he is very important and he needs to be ready to help the team when the opportunity arises, which could be very soon."
Stoke head into the game buoyed by a 2-0 home victory over struggling Sunderland last weekend.
Mark Hughes' side are unbeaten in their last three top-flight games, but have only won once on their travels in the league and that was at West Ham back in August.
Defender Robert Huth (knee) and midfielder Marko Arnautovic (hamstring) have been ruled out of the trip to Goodison Park, but midfielder Stephen Ireland (shin) is back in contention.
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