Colena is out of contract next summer and is 32, which means he may be drawing near to the end of his playing days.
Director of football Marcel Brands has already talked with the club captain about keeping him around when he retires.
"They have so much experience, they love the club, they know the club, they know what's necessary at Goodison.
"I will do everything to keep these guys on board to help me to move the club forward."
Brands added: "What you just said, he's not only a fantastic player but a great character in the dressing room, a great professional.
"I'm now already in talks with him to get him involved in, let's say, things off the pitch.
"He's definitely someone I really want to keep in the club after he finishes his career. He's a great example for everyone."
Brands concluded: "He is natural, he's normal. He's the guy that will not change in the future, I think Leighton [Baines] is the same.
"I think we have a lot of those good guys in the club, and it is so important to keep these kind of guys on board."