Yates is also in discussions with striker Darryl Duffy about a possible future with the Robins, who came up short in the League Two play-offs for a second successive season.
Darren Carter, Bagasan Graham and Harry Hooman will be released in the summer at the end of their current deals.
Yates told the club's official website: "It's the part of football that no manager enjoys.
"I want to thank Darren, Harry and Bags for their service to the football club since being here. Darren is the more experienced and we cannot pay him what he would like but I'm not closing the door on him completely.
"Harry is a fit and strong lad but he has been unlucky with injury despite having a decent start to the season. He is another one I won't shut the door on and, if he isn't sorted by pre-season, then we have invited him back to train with us."
The Town boss added: "I'm still talking with Darryl and his agent about his future so we'll see what happens with that over the next few days.
"The other players have been offered deals and we'll have to now see what happens over the coming days and weeks. I have spoken to Russ Penn and we have verbally agreed on a deal. He is a player I trust and I want him as my captain next season."