The 24-year-old Uruguay international is set to make a ??2m move to the Stadium of Light after spending a loan spell with the Black Cats last season.
Talks are ongoing and Sunderland are hopeful of reaching a successful conclusion within days.
Coates, who has just a year of his contract at Anfield remaining is currently enjoying a break after Uruguay’s involvement in the Copa America.
If the deal is completed, Coates will become Sunderland 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 also in his sights.