Alvarez joined the club 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,” He 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 they are 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," he added.
“But I am happy here.”