The 24-year-old is free to move clubs this summer although the Cobblers would be due a compensation fee for the goalkeeper should he decide to leave Sixfields upon the expiry of his contract and not sign the new deal that is on the table for his services.
Coventry are expecting to lose Keiren Westwood shortly and want a replacement for the Irish international with the favourite up until now having been Joe Murphy of Scunthorpe United.
“If a Championship-level club comes in for someone and they’re out of contract then you have to wish them well,” Northampton manager Gary Johnson told the Chronicle & Echo.
“He never let me down, Dunny, so if he does stay then I will be happy to have him here as my first-choice goalkeeper."