The future looks bright at Goodison Park with the likes of Coleman, Ross Barkley, James McCarthy and John Stones at the club, and Martinez wants these exciting youngsters to grow together.
Coleman has reportedly attracted interest from the likes of Manchester United, Arsenal and Manchester City, but Martinez has dismissed suggestions of a summer departure and insisted plans are in place to arrange new contracts.
He said: "We won't offer encouragement to any club over Seamus. He is on a long-term contract and we want to ensure we grow together and we need players like Seamus.
"Yes, it is the intention to offer him a new contract. We are already thinking about Seamus, Ross (Barkley) and John Stones. We want to reward them, even James McCarthy.
"That is something we will look at this summer. They are players with long-term contracts. It is not a decision just to keep them at the club; it just highlights the next step of their development and rewards them for their performances.
"Seamus has got a long-term contract. James and Ross are the same. But we want to reward them."
Martinez is convinced that his young players will go from strength to strength over the next few years and hopes they will agree to extend their deals.
He said: "We hope they will feel excited about developing with the football club and I think with the young players we have got in the club - Seamus, Ross, James McCarthy - they are footballers I believe to be of the highest, highest level.
"We need to grow together. The way we work at the club, there is a structure in the salaries and everything goes down to your role at the club."