Alvarez joined Inter in 2011 from Velez Sarsfield but has only played 32 times in Serie A due to a number of injuries.
“It is my desire to stay here. I want to make a career in Europe," Alvarez told ESPN. "When I started at Inter I knew it would not be easy, but this experience is strengthening me as a player and as a person.”
On the interest from River Plate, he stated that while it is a big club, he would prefer to remain with his current club in Italy.
“My greatest desire is to remain at Inter. River Plate are a great team, perhaps the best in Argentina," Alvarez said. “But I am happy here.”