Robinho's future at Milan is uncertain, with the Serie A club needing to sell an attacking player in order to fund a bid for Manchester City's Carlos Tevez.
Milan vice-president Adriano Galliani recently confirmed talks had taken place with Santos, but the Brazilian club have stated that a deal for Robinho is too expensive.
That has opened the door for Cruzeiro to declare an interest in the 29-year-old and director of football Alexandre Mattos is prepared to make every effort to sign Robinho.
"We had talks about 15 days ago and I made it clear that, for Robinho, Cruzeiro will not spare any effort to sign a big-name player like him," Mattos told Radio Itatiaia.
"We want Robinho. Cruzeiro has even talked about values with him.
"He made it clear that Santos are his priority since they sold Neymar. That's what he wants. But I made it clear the doors are open and that Cruzeiro will not spare any effort."
Robinho started his career at Santos before leaving for Real Madrid in 2005, and he returned to his old club on loan in 2010 before linking up with Milan from Premier League side City later that same year.