In July 2013, Álvarez Balanta officially signed his first senior contract with the club on a three-year term deal with a $30 million release clause.
Álvarez Balanta noticeably put on a man of the match performance in the 2013 Copa Sudamericana match against San Lorenzo. Throughout the match, he was praised for being "impassable".
In September 2013, it was reported that Barcelona had taken interest in Álvarez Balanta, and they plan to watch the player to evaluate his development. It was also mentioned that Álvarez Balanta could possibly be a successor to Barça's aging defender Carles Puyol, but that River Plate would require €50 million in any transfer deal. Weeks later, however, River Plate brought down his release clause to €15 million.
Álvarez Balanta attracted the attention of the Colombian Football Federation in May 2013 during his time with River Plate. He was called to be part of the U-20 squad for the 2013 FIFA U-20 World Cup in Turkey. Due to injuries and the factor that he had yet to sign his first professional contract, River Plate stated that they would not allow him to partake with the national youth squad if he does not meet with his youth contract before signing a senior contract. In June 2013, it was confirmed that River Plate would not allow him to take part in the U-20 World Cup.
On 7 November 2013, Álvarez Balanta received his first senior call-up to play friendlies against Belgium and the Netherlands. On his second call-up, Álvarez Balanta made his international debut, coming in at the 65th minute in a friendly against Tunisia.