With Elliott's contract expiring in the summer, the club are hoping to sell now rather than see him leave on a Bosman free transfer.
It is believed that a League One club - possibly Huddersfield or Leeds - had a £100,000 bid with added incentives accepted, but Elliott turned down the 2½-year contract on offer. Sheffield Wednesday are also rumoured to be interested.
Elliott joined City for £230,000 in 2002, and has been the club's top scorer in three separate seasons, achieving promotion twice and earning a place in the club's all-time top scorers list with 65 league goals.