The 28 year old has a year left on his contract and made 35 appearances for Burnley in the season just gone.
He has also played for Torquay and Stoke City.
City have also been linked with Sunderland's out of contract striker Tommy Miller.
According to the BBC, Coventry along with Hearts, Stoke and Sheffield Wednesday will speak to Miller who will pick which club he wants to join on June 20th. Miller has played for Hartlepool and Ipswich.