Mills is reported to have met City officials yesterday and agreed in principle to a move on a free transfer.
When he completes details on his current Leeds contract, Mills will report for pre-season training with his new team-mates next week.
The England international defender spent most of last season on loan at Middlesbrough, winning a league cup medal in the process.
His agent, Neil Featherby, told BBC Radio Leeds: "Negotiations are at a delicate stage but we have been speaking since the middle of the week. There has been a lot of interest in Danny with clubs knowing he is available on a free transfer."
When he completes details on his current Leeds contract, Mills will report for pre-season training with his new team-mates next week.
The England international defender spent most of last season on loan at Middlesbrough, winning a league cup medal in the process.
His agent, Neil Featherby, told BBC Radio Leeds: "Negotiations are at a delicate stage but we have been speaking since the middle of the week. There has been a lot of interest in Danny with clubs knowing he is available on a free transfer."