Deals for White and Cousins .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.
"I have made contact with their agents, expressed our wish to retain the pair and put contract offers in front of them."
He told the official website on Friday morning: "They are two players I would like to keep.
The duo's current deals end this summer and Joe Dunne has begun proceedings to extend their stays with the U's.
The U's have offered new contracts to John White and Mark Cousins as preparations begin for next season.
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."
The official website will be the place to find the latest transfer news throughout the summer so keep an eye on cu-fc.com.