Both Premier League clubs have made moves for the Uruguayan central defender, who is currently playing in his homeland with Nacional.
The 20-year-old revealed earlier this week that he expected a decision to be made on his future by the weekend.
Now Coates has confirmed that Liverpool would be his preferred destination, mainly due to the influence of compatriot Luis Suarez, who is currently at Anfield.
"I'd prefer Liverpool to Manchester City, but would need to see what they have to offer and would compare them," Coates told Ovacion.
"But having the help of Luis Suarez would be very important. I will be going to England, we are just missing a few details now.
"The Liverpool offer ticks all boxes, so fair to say it's a done deal. Luis's success is important for me as another Uruguayan joining.
"Liverpool is a club with great tradition and history, and Luis would be a great help to me. Suarez has spoken to Kenny Dalglish and his managers about my signing.
"He said it will be great having a Uruguayan with him, we chatted for quite a while, as he is someone I know well."
Coates shunned offers from elsewhere in Europe and admits he was waiting for the Premier League.
"My intention was always to wait, there were many rumours that I wanted England, but nothing concrete. Fortunately we have now received the offer," he said.