Leeds have identified him as “a top target” for the forthcoming transfer window. The Whites are hoping to wrap up a move as quickly as possible after the end of the Championship season.
It has been a disastrous campaign for Leeds, and Paul Heckingbottom has hinted that the club would involve heavily in the summer transfer market.
Swansea City will listen to bids for the 26-year-old but it all depends on whether they avoid relegation and retain their Premier League status.
Bartley, who signed a new contract at the Liberty Stadium in August, has rarely featured for the Swans. However, Carlos Carvahal could retain him if Swansea drop into the championship next season.
He made a strong impact for Leeds, on loan, last season, where he started 45 league games and helped the Yorkshire outfit compete for a play-off position.
Bartley is understood to be open to a return to Leeds having featured only four times in the Premier League since moving back to Wales.