Monaco vice-president Vadim Vasilyev has said Atletico Madrid are interested in Fabinho, and admitted other key players could also leave the club this summer.
Fabinho, 24, was linked with Paris Saint-Germain and Manchester United in the past, and Vasilyev has now revealed that Monaco will sell the Brazilian should they receive a suitable bid in the close season.
"Yes," he told SFR Sport. "We owe this kid because he's been here four years and it's been promised to him.
"But we have to wait for the right offer because we'll never let a player leave if the offer isn't satisfactory for Monaco... Atletico are not the only club who have shown an interest."
More major departures are expected at Monaco, who finished second in Ligue 1 this season after being dethroned as French champions by PSG.
Manchester United are reported to be keen on full-back Djibril Sidibe but Vasilyev said that the 25-year-old is unlikely to consider a transfer until he returns from World Cup duty with France.
"There is interest in him," Vasilyev said. "I've heard [the Manchester United rumour] talked about. But we don't have anything concrete on the table.
"There are really a good few clubs circling around him. I think in his case, too, we have to wait for the World Cup. I don't think it's the time to talk about a transfer before the World Cup."
Monaco lost Kylian Mbappe, Benjamin Mendy, Bernando Silva and Tiemoue Bakayoko last summer but managed to keep hold of midfielder Thomas Lemar despite a reported €100 million bid from Arsenal.
Having helped Monaco secure a return to the Champions League group stage, however, Lemar's future with the club now appears less certain.
"First and foremost, he's a top player," Vasilyev said of the France international. "I'm convinced that he'll have a good World Cup. And then we'll discuss the price."
Striker Radamel Falcao, who finished with 18 league goals this season, is another player who could be on his way. The Colombian reportedly attracted interest from China earlier this year, and Vasilyev indicated that the 32-year-old's prospects would also be discussed after next month's World Cup in Russia.
"I think we really have to wait for the World Cup and then see what happens," he said. "I'd like to keep him but if we wants to go elsewhere and there are good offers then we'll talk about it."