The 24-year-old has been linked with a move to England in the past, with Cruzeiro forced to dismiss reports that Manchester United had agreed a fee for the former Cortiba man in November.
Ribeiro's agent, Robson Ferreira, refused to name the side chasing his client's signature, and, despite the initial offer being rejected, is keen for further talks to see if an agreement can be reached.
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“We took the proposal to Cruzeiro, we talked and arranged a new meeting for the next few days. The club want him to stay and the player also wants to help Cruzeiro in the Libertadores. We are trying to unite all interests.”
Cruzeiro director of football Alexandre Mattos, meanwhile, is keen to hold onto Ribeiro after confirming a new bid, and insists it would take a large offer for the Brazilian club to consider selling – and they would also need to find a replacement first.
“Everton was one of the players that came to Cruzeiro with potential and, together with his team-mates, turned that into reality,” said Mattos.
“He won individual awards. He is happy, but there is no offer that makes the president change his stance. Yesterday one more arrived from an English club to which Cruzeiro said 'no' immediately.
“It could be that an offer arrives that Cruzeiro understands would be irresponsible not to accept. The important thing is knowing to get a suitable replacement. When something happens either way, we will have a replacement identified.”