The Black Cats are close to tying up a £2million deal for the 24-year-old Uruguay international, who had a loan spell at the Stadium of Light last season.
Press Association Sport understands talks are ongoing and that the club is hopeful of reaching a successful conclusion within days.
Coates is currently enjoying a break after Uruguay's involvement in the Copa America, but with just a year of his contract at Anfield to run, is expected to leave this summer.
Should Sunderland manage to get it over the line, he will become head coach Dick Advocaat's first signing as he attempts to re-build his squad to avoid a repeat of the troubles of the last two seasons.
Coates was signed on loan by compatriot Gus Poyet during his spell in charge on Wearside, and although he struggled to make an impact during his early months in the north-east, he came to the fore as the Black Cats launched another ultimately successful safety bid at the end of the campaign.
In total, he made just 13 appearances for the club, but played every minute of the final six games from which Sunderland took nine points to ease themselves out of trouble.
Advocaat is looking to sign up to six players of proven quality this summer with West Ham midfielder Stewart Downing, who is also attracting interest from former club Middlesbrough among others, also in his sights.
Source : PA
Source: PA