Former Manchester United midfielder Gibson has yet to feature this season due to a knee problem.
Kone missed Everton's win over Chelsea last weekend.
"I'm very happy with how Darron Gibson and Arouna Kone have progressed with their injuries and they could make the squad this weekend," Martinez told a press conference on Thursday.
"Steven Pienaar is 50-50, as he has recovered very well but we need to be careful.
"Romelu is ready to be available. He's played a lot of football this season and he's got used to his teammates in the past week and trained very well.
"Antolin Alcaraz (hamstring) is still recovering and won't be available. But, other than that, everyone is fit and available for the game.
"I was really pleased with the level on Saturday and now we have to use all our options in the squad and be as strong as we can. We've got three games in a short space of time, so we need everyone ready and available."