Colchester have offered new contracts to John White and Mark Cousins as preparations begin for next season.
The duo's current deals end this summer and Joe Dunne has begun proceedings to extend their stays with the U's.
He told the official website on Friday: "They are two players I would like to keep.
"I have made contact with their agents, expressed our wish to retain the pair and put contract offers in front of them."
It is no secret that Dunne will be working with a reduced budget in the coming season and he said he will have to build his squad carefully.
He added: "I will have to look closely at where I'm spending in terms of building a squad for this season because of the reductions but that's a challenge I fully understand and one that I'll get on with."
Matt Heath and the U's have parted company, bringing to the end a five year association with the club. The central defender's current contract runs out this summer and Joe Dunne has decided not to extend it.