Chester are waiting to hear back from Peterborough on their offer for Dean Holden.
Posh boss Barry Fry had claimed there had been no approaches for the former Bolton defender, but The Blues have now stepped up their interest.
Peterborough's poor financial state means Fry may have to sell one of his most prized assets.
Chester are also hoping to resolve the futures of Michael Branch and Wayne Brown, who both have one year remaining on their current deals, in the near future.
"We have the situations surrounding Michael Branch and Wayne Brown, both of whom have 12 months of their contracts to run with us," chairman Stephen Vaughan told the club's official website.
"Discussions and decisions will have to be arrived at with them."
The long-term futures of Tom Curtis, Sean Hessey, Abdou El Kholti, Carl Regan, Luke Dimech and Ryan Brookfield, all of whom are out of contract, are set to be announced soon.
Meanwhile, Kelham O'Hanlon has left Chester's management team.
The former goalkeeper had been one of Mark Wright's right-hand men, but following the arrival of Graham Barrow as assistant manager he has decided to leave.