Bernard was part of the Mineiro side that secured the club's first Copa Libertadores title following a second leg fightback against Club Olimpia.
Arsenal are thought to hold an interest in the winger, with Shakhtar Donetsk and Porto also said to be keen on securing the 20-year-old's services.
However, any potential suitor will have to pay a hefty price to lure Bernard away from Belo Horizonte, with director of football Eduardo Maluf confirming their asking price for the Brazil international.
"The president has made it clear that if there is a €25m (£22m) offer, he will sell Bernard and we will sign another player," he said.
"Otherwise Bernard stays. He is young and can leave at the end of the year."
Maluf also dismissed rumours linking Bernard to Arsenal.
"Arsenal have denied the Bernard rumour," he added.
"He is the great player of the moment."
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