City want to bring the former fan favourite back to Ashton Gate after being released by Villa at the end of the season.
The 31-year-old is a free agent after leaving Aston Villa following their promotion to the English Premier League.
The former Ghana international made 24 league starts for the club but was not enough to help him stay.
Circling reports in England have claimed on Tuesday that the winger is hot in demand with a number of Championship side interested in his signature.
Bristol City are set to be leading the chase for their former star man with Nottingham Forest and Millwall also interested.
Leeds United are also lurking to pounce while he could make a return to Riverside after an interest from former clb Middlesbrough.
Adomah made 136 appearances for the Robins from 2010-2013, after arriving from Barnet, and was a teammate of head coach Lee Johnson during the 2010/11 season.
Adomah, who still owns a house in Bristol, would ideally like to remain in the Midlands for personal reasons but, at the same time, is excited by the prospect of returning to City given the project being undertaken by Johnson.
Having been part of two promotion-winning squads at Middlesbrough and Villa, he wants to maintain that level of expectation and pressure.