Coleman is reportedly in demand, having led Wales to their first international tournament in 48 years, but talks with the FA of Wales regarding a new deal have reached an impasse, the 45-year-old told BBC Sport on Monday.
The former Fulham boss is out of contract in the summer and Swansea, who it is claimed are ready to part company with interim head coach Francesco Guidolin at the end of the campaign, are reportedly considering an approach.
Coleman hails from the South Wales city and made almost 200 appearances for the Jacks between 1987 and 1991.
Villa are also said to be keen on Coleman, with Remi Garde expected to be sacked this week.
According to the Birmingham Mail, the Villains are looking to hire a British coach as Garde's replacement, with Garry Monk and Tony Pulis the latest names to be linked after Nigel Pearson, Sean Dyche, Brendan Rodgers and David Moyes.
Meanwhile, the Sun reports that a return to Spain, where Coleman managed Real Sociedad previously, could also appeal to the former Wales international.