The 20-year-old, who can operate at centre-half or at left-back, only penned his first senior contract in July.
He has, however, been drawing admiring glances from Europe for some time, with Inter Milan reported to have tabled an offer after seeing him make just five appearances.
Barcelona are now said to have joined the hunt, with the Primera Liga giants in the market for potential stars of the future.
Balanta claims to be unaware of any official contact from Catalunya, but hopes there is substance to the rumours as he would make history as the first Colombian to turn out for Barca were a deal to be done.
He told Sport: "As far as I know, there hasn't been a Colombian playing for Barcelona. I would be the first one in the history of the club.
"If it's true, I would be very proud. If it's not, I will try to keep doing things like I have done up until now.
"I have played a few games in the first division and I have to keep going this way - working hard, doing things correctly with effort and sacrifice, in the same way as all of my team-mates."
On the prospect of playing alongside Gerard Pique at Camp Nou, Balanta added: "He is my idol. He is a player who does everything well.
"I like him and he is a defender that likes to attack a little bit, which I also like to do sometimes at River."