The 23-year-old defender has been on the sidelines since August with an anterior cruciate ligament injury, but still retains hopes of being fit for the World Cup in Brazil.
And to aid his recovery, reports in Uruguay suggest he will move to Nacional to speed up his recuperation, a fact Coates himself admits is appealing.
"It would be beautiful to join Nacional and complete my recovery in Uruguay with my family and friends," the centre-back told Radio El Espectador 810.
"The negotiations can be hard sometimes, and we have to wait a bit."
Liverpool will reportedly pay all of Coates' wages if he is loaned to Nacional, and the Montevideo outfit will not have to contribute anything to get him on loan.