Peterborough will attempt to re-sign defender Craig Alcock, but have given up on keeping forward Danny Swanson.
Alcock had been released but, with right-back Mark Little set to join Bristol City, has been offered a deal.
"I have got a couple of deals lined up for right-backs," Posh director of football Barry Fry told BBC Radio Cambridgeshire.
"But the gaffer said Craig hasn't been fixed up yet and we put something to him on Monday."
Alcock, 26, played 39 times last season, starting the campaign at right-back before appearing more regularly at left-back and centre-half.
Fry confirmed that Little, 25, opted to end four years at London Road by agreeing a deal with League One rivals Bristol City two weeks ago.
Swanson, meanwhile, was also offered fresh terms at Posh following a mixed season that saw the 27-year-old Scot play 49 times.
"I thought he was going to go to Aberdeen but I spoke to him recently and he felt he had a couple of offers from League One clubs which were more tempting," he said.
"We made him an offer and he turned it down and we wish him well."