The Uruguay international has been linked with a number of English clubs in recent months but the only firm interest in his services has come from an unnamed Italian side
The Uruguay international played a key role in the Rossoblu's ninth-placed finish in Serie A last season and is widely expected to leave the Renato Dall'Ara this summer, with a plethora of Premier League clubs said to be chasing the 21-year-old.
Zanzi explained, though, that it is an Italian team that is currently at the head of the queue, but even they have yet to meet Bologna's valuation of the player.
"To take him, one must begin [the bidding] at €20 million," the Bologna official told Radio Kiss Kiss. "At the moment there are two open negotiations for the player that, however, did not satisfy our expectations, neither ours nor his.
"Let's say that in Italy, however, there is one club that has taken concrete moves to get to the player.
"If offers arrive that we deem valid then we will certainly consider them. If not, Gaston will remain with us.
"Our expectations are high because we believe that those who take Ramirez can easily absorb an investment that initially seems onerous. We have come up with a figure and for now nobody has matched it."
Ramirez, who joined Bologna from Penarol in 2010, netted eight times in 33 Serie A appearances last season.