Williams is out of contract at Charlton this summer, and the former Crystal Palace midfielder will become a free agent.
The 25-year-old midfielder joined the Addicks on a short-term contract in the January transfer window after leaving Premier League club Palace.
The Wales international helped Charlton clinch promotion to the Championship from League One via the playoffs.
According to The Daily Mail, Swansea in the Championship want to bring the attacking midfielder to the Liberty Stadium on a free transfer.
Good signing for Championship clubs
Williams failed to make a massive impact during his time at Palace, but the Welshman is a very good midfielder, and he will be a smart signing for any club in the Championship aiming to challenge for promotion to the Premier League.
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