The 16-year-old has been shining at youth and reserve level for River but is yet to make his first-team debut for the Argentine club.
According to SPORT, his displays have attracted the attention of a number of clubs, including Barcelona, with the Catalan giants said to be keeping a close eye on his development ahead of a future move.
The report claims that there is a €30m (£25m) release clause in his contract which expires in December 2026, although River would be prepared to negotiate if they were approached regarding a move for the youngster.
Esquivel largely operates as a right-sided attacker, and he has made four appearances for River Plate's second team this season, providing an assist in his team's clash with Rivadavia II at the end of August.
Barcelona 'interested in Argentine youngster Esquivel'
The youngster has also been capped at Under-15s and Under-17s level by Argentina, and he is being tipped as a future star.
Barcelona already boast some of the best young players in world football, with Pau Cubarsi, 17, Gavi, 20, Pedri, 21, and Lamine Yamal, 17, among those who are starring for the Catalan giants.
At 24 years and 185 days, Barcelona's starting XI against Bayern Munich on Wednesday actually had the lowest average age in a Champions League fixture since their game with BATE Borisov in November 2011.
New head coach Hansi Flick has shown a willingness to trust youngsters since his arrival, with Marc Casado also among those to receive plenty of football this season, benefitting from the club's injury problems.
The future looks bright for Barcelona due to their young talent
Flick was full of praise for Casado after the midfielder's performance against Bayern, with the 21-year-old playing an important role in his side's 4-1 success over the Bundesliga giants.
"It's incredible if you know that Casado comes from Barca Atletic and you see the level he has now. He's incredibly good defensively and with the ball at his feet," said the team's head coach.
"It's La Masia. Everyone in the stadium sees the quality of these players. You could see when we had confidence, in the second half, how we passed the ball around, it was incredible. Everyone was happy, including the staff."
Barcelona are currently preparing for Saturday's El Clasico against Real Madrid, and the Catalan side hold a three-point lead over the reigning Spanish champions at the top of the La Liga table.