The Argentine star is much coveted by the club's Brazilian rivals, and the Tricolor will break the bank to try and convince Cruzeiro into releasing him
The Argentine has been one of the stars of Serie A since joining the Raposa from Universidad de Chile in 2010, and Cruzeiro's recent struggles with form have raised the possibility of a move to one of the side's Brasileirao rivals.
Sao Paulo have shown strong interest in the playmaker, and according to Cruzeiro director of football Dimas Fonseca, a big offer has already arrived on the club's table.
"Sao Paulo have made us a proposal worth approximately €10m, plus the loan signing of three players that we can pick - with the exception of Rogerio Ceni, Luis Fabiano and Lucas," the director told Radio Itatiaia.
"We have talked about a couple of names, and [Sao Paulo] have sounded out the players to see their interest in coming to Belo Horizonte, but the value is still less than what Doctor Gilvan [Tavares, club president] stipulated."
The Cruzeiro chief has previously stated that he would hold out for €15m to release Montillo, while Sao Paulo's city rivals Corinthians have also been reported as possible suitors.