Dominic Vose, Ryan Dickson, David Wright and Mark Cousins are all currently mulling over new deals offered to them by the U’s.
U's boss Dunne said: “I’ve spoken to them all again over the last few days and they all know where they stand.
“I understand that they need to consider their own options and it’s about doing the right thing for both parties.
“I think dialogue will be important between everyone and things will become a lot of clearer in the next couple of weeks.”
Dunne has praised defender Tom Eastman, after he scooped the Player of the Year and Players’ Player of the Year awards.
“Tom has played a lot of games for us this season and along with the goalkeeper and the rest of the back four, has done well," said Dunne, who attended the LMA awards winner in London last night.
“The centre-back position is very difficult for a young player but Tom’s maturing into a very good young player.”
Meanwhile, Dunne said there is no fresh update on his pursuit of Crystal Palace defender Alex Wynter.
For more on this story and all of the latest Colchester United news, including Joe Dunne's analysis of the U's 2013-14 season, see Tuesday's Daily Gazette.