Andy Myers is being linked with Gillingham.
Defender Myers, among a clutch of senior players that City have released, is understood to be keen on a return south.
And the Kent club have revealed that he is on their list of possible summer targets.
Gillingham are also chasing Ian Cox, freed by Burnley, and former Watford skipper Neil Cox.
Boss Andy Hessenthaler said: "They are all good players otherwise we wouldn't be looking at them. We need to strengthen defensively."
Hessenthaler has already made offers to the two centre-halves. He sees the versatile Myers as a possible replacement for left-back Roland Edge, who is currently in contract talks with chairman Paul Scally.
Myers, 29, joined City for £800,000 from Chelsea in July 1999 ahead of their first Premiership campaign. He made 99 appearances in four seasons with the club, scoring three, and was named player of the year in 2001-2002.
But with his wages believed to be around £8,000 a week, he could not be fitted into the new pay structure that has been introduced since administration.
Meanwhile, City fitness coach John Roe has signed a new one-year contract.
Roe, from Addingham near Keighley, has been working with the club since December.
Boss Nicky Law said: "He's come in and done a great job as well as proving very popular with the players. That's a big part of it as well because when you bring someone new into this environment they need to be able to fit in.
"Since he came to the club, we've looked stronger, fitter and quicker."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article