Barca have refused to deny the rumour, with vice-president Sandro Rosell saying: "I refuse to answer the question of whether we have received a bid for Ronaldinho.
"I have a degree of fear concerning Chelsea because if it is true that Abramovich is willing to invest further hundreds of millions of pounds in the transfer market then his aim will be to buy one of our best players.
"With Abramovich you know he has the money whereas with, say Real Madrid, you don't know it to the same degree.
"Barcelona remains a 'sick club' because we still owe £164 million but I think we are imposing financial control and that we are on the road to recovery.
"So I hope that it is one thing for someone like Abramovich to move for one of our players and quite another that they accept his offer."
"I think that the great players are deeply involved in our rebuilding project and want to see it continue," he added in an interview with the Sun.
"I mean, look at Arsenal, we know that Arsenal received a £50 million offer for Thierry Henry and they said no.
"That is the kind of decision I would say we would take with Ronaldinho.
"I view it impossible that he only stays here for one season like, say, Romario did.
"I think that Ronaldinho is deeply attached to the club and the city."