Liverpool are currently in advanced negotiations with the 20-year-old Uruguyan's club Nacional over the deal.
The £12m-rated centre-back impressed in Uruguay's Copa America triumph in July and is keen to join international team-mate Luis Suarez at Anfield.
He would be Liverpool manager Kenny Dalglish's sixth signing of the summer.
Dalglish is keen to strengthen his defensive resources after Greek defender Sotirios Kyrgiakos left for Wolfsburg on a free transfer and 6ft 6in Coates, 20, is seen not only as another quality addition but also a sound investment for the future.
Manchester City have been strongly linked with Coates but Liverpool are now firm favourites to add Coates to Dalglish's other summer signings Jordan Henderson, Charlie Adam, Stewart Dowing and Jose Enrique.
Adding another central defender became Dalglish's top priority after completing deal with Newcastle United for left-back Enrique - and talks are progressing to conclude a move for Coates.
