The 20-year-old, who has been linked with a number of European clubs, is regarded as one of the best young defenders in world football.
"Balanta is worth €15m (£13m). He is a great player with a great future. We would listen to offers for him, but Barca have made not official offer to us for him," Solassi told Esports COPE.
"I think that Balanta would be liked by Tata Martino. It would not seem odd to me if Barca are interested in him. He is a player that will come good whichever team he plays for.
"Balanta is not like [Javier] Mascherano nor like [Gerard] Pique. He is a different sort of player with more presence. He is a strong defender, is good on the ball and knows how to play going forward."
Alvarez joined River from Academia in 2011.