Baines has made two substitute appearances after nearly seven months out following two operations on his ankle.
Toffees boss Roberto Martinez said: "After the Middlesbrough game he took a little bit of a knock and it took him probably 24 hours to get back to normal. After the game against Crystal Palace, he had no reaction.
"We need to be very much aware when a player's out for such a long period, you cannot just expect to come back and be perfect for 90 minutes.
"But I was delighted with the way he reacted after the game on Monday. He's getting very, very close to being able to challenge for a start."