The 30-year-old tested positive for an as yet unnamed substance in both his A and B sample after a World Cup qualifier against Venezuela on March 31st.
Correa played the final 31 minutes of the game after coming on to replace Javier Chevanton in a 3-0 win.
The former Atletico Madrid hit-man is now likely to face a lengthy ban from Fifa, but Uruguay coach Jorge Fossati insists the player will be supported.
"Now the most important thing, and the only thing that we can do, is to be close to the person that is involved in this," Fossati stated.
"We have to help him and give him all our support.
"We can't be blind in respect to these kind of things that are happening everywhere.
"This isn't something that happens only in football so we have to help the person that has a problem like this. It's a problem that we all have to fight against."
