According to Wales Online.
Swans boss Brendan Rodgers is eager to bolster his front-line options ahead of a second season in the Premier League.
And it is thought Ghana winger Adomah has been identified by the Northern Irishman as a player who can add competition to the wide roles after catching the eye at Ashton Gate.
Adomah, 24, has already attracted the interest of a host of Premier League clubs over the past 18 months with the Robins having to issue ‘hands-off’ warnings to potential suitors in January.
But Swansea could be ready to test Bristol City’s resolve with an initial bid of around £2m for a player who has two years left to run on his current deal.