Coates spent last season on loan at the Stadium of Light. establishing himself in the first-team under Dick Advocaat, and the Chronicle has claimed that they will be moving for him on a permanent basis at the end of the Copa America.
The 24-year-old centre-back made 13 appearances in all competitions last term, making an impact when Advocaat was named head coach, and the Dutch boss is a keen admirer of him.
Coates has failed to ever establish himself at Anfield, despite signing for Liverpool in 2011, and with just one year left on his contract, a summer transfer is expected.
The Black Cats have been linked with making a move for Coates on a permanent deal for the last few weeks, and the latest report indicates that they are preparing a deal, and will approach Liverpool at the end of the Cop America.
The centre-back is currently away in Chile with his Uruguayan teammates for the tournament, and whilst he will be hoping to help his nation retain their 2011 trophy, Sunderland will be attempting to create a deal that the Reds will accept.
It is likely that Liverpool will have no qualms about selling Coates, with him making just 24 appearances since his 2011 arrival - of which only six were Premier League starts - and with his contract expiring next summer.