But their interest in Fabio Borini reportedly remains, with the club at the centre of a summer-long transfer saga concerning the Italian.
Liverpool are ready to let the 23-year-old leave and Gus Poyet has confirmed he wants to sign the striker on a permanent deal.
Like Coates, Borini spent last season away from Anfield - on loan at Sunderland.
However, the Black Cats are also now said to have enquired for Manchester United's Danny Welbeck, an alternative to Borini.
Sunderland should have more luck landing Coates, though, with the centre-back firmly out of the first-team picture at Liverpool.
Indeed, the season before last - before the Reds signed Mamadou Sakho and Kolo Toure (with Dejan Lovren also having now been brought in this summer) Coates made just five appearances.
The Uruguayan played less minutes than any other Liverpool centre-back - and was then shipped out on loan the following campaign.
Poyet may just get his man, then, but it remains to be seen whether Borini will join him, too.