River Plate President Rodolfo D’Onofrio confirmed Leonel Vangioni to Milan, while Napoli and the Rossoneri like Emanuel Mammana.
The Argentine club has been involved in fraught negotiations over the January transfer window, though no transfers were completed.
There was an exchange of angry statements with Fiorentina after the €9.5m deal for defender Mammana fell through.
“Mammana is a very important player,” River Plate President D’Onofrio told Calciomercato.com.
“The club plans to keep its most representative players so as not to weaken the side. Clearly if an offer arrived that was in line with his potential, then we’d take it into consideration.
“Is he valued at €10m? It is not fair to make prices in this context. He certainly has a high valuation, as is suited to a player of great promise.”
There are reports Milan and Napoli have now joined the race for Mammana over the summer.
“We have an excellent rapport with Milan. We are bonded by ties of respect and admiration going back many years and we’ve never had problems with them.
“Having said that, we have never directly discussed Mammana, but I won’t rule out the idea they might’ve talked to the players’ representatives.
“It’s premature to talk about Napoli, as they have not contacted us directly either.”
The Rossoneri do seem to have a deal in place to sign River full-back Vangioni as a free agent in June.
“We talked to Milan about Vangioni. I believe he will go to Milan in June, when the contract tying him to our club expires.”