Jose Enrique is back in the picture, but Joe Kinnear was forced to rule fellow full-back Habib Beye.
Kinnear admits he has liked what he has seen of Ameobi this week and he hinted he is ready to partner the 26-year-old striker with Michael Owen.
Kinnear: "I have two choices up front for a partner for Michael - Shola Ameobi or Xisco. I will probably give them 45 minutes each, but I am leaning towards starting off with Shola.
"This will be a big opportunity for him and I hope it is not a lost opportunity.
"They tell me he has 46 goals for us and this is more than anybody else in our squad at the moment.
"I have had a good talk to Shola this week and I have told him he has the size, power and pace to go out there and do it, and this is what I am looking for him to do tomorrow.
"I sat down with Habib Beye and had a long chat with him, but he feels he is not quite right and he is not going with us to Everton.
"But at least Charles N'Zogbia, who has not trained much this week after picking up that knock against Blackburn, is now OK, and we are delighted to have Danny Guthrie back from suspension.
"You want to get off to a winning start. There's nothing I want more than to kick-start my reign here with a victory.
"We really need to get ourselves out of the position we are in. The last thing we want is to be in the position we are in now during the international break, with players moping around.
"There would be a feelgood factor for the following two weeks if we were to go to Goodison and get a decent result."