The Robins have not cooled on their interest in Matthews despite little activity since his loan spell ended.
The Bristol Post reported two days ago that Matthews was the club's number one target despite rumours on the contrary, with Northern Ireland defender Conor McLaughlin seen as an alternative.
It was also reported in The Chronicle last week that Matthews' departure was dependent on a full-back coming in the other way, with Billy Jones the only current alternative at full-back as the Black Cats are reluctant to meet Tottenham Hotspur's £5 million valuation of DeAndre Yedlin.
Adam Matthews has made just one appearance for Sunderland
However, the Echo now suggest that Bristol City may swoop regardless, with Matthews one of a number of players facing the cull at the Stadium of Light.
Matthews was omitted from Sunderland's pre-season tour squad to Austria along with Liam Bridcutt, Will Buckley, Jordi Gomez and Charis Mavrias, despite returning to training with Sam Allardyce's squad two weeks ago.
Jordi Gomez is also unwanted at Sunderland
The report outlines that Matthews does not have a future at the Stadium of Light, having spent much of last season on loan in the Championship with Bristol City.
Matthews was signed from Celtic for £2 million last summer, but was carted off to the West Country after struggling to make an impact with his new club, making just the one appearance before beginning his temporary departure back in March.
Adam Matthews left Celtic for Sunderland last summer
The Welshman made nine appearances for City during his time at Ashton Gate and he may well add to that should the Robins build on their interest and make Sunderland an offer.