"Paris St Germain have an offer from us on the table," Barcelona president Joan Laporta told the club's website on Wednesday.
"It's an important offer and it's the final word from us. We're sticking."
According to Laporta, Manchester United made a counter-offer for Ronaldinho late on Tuesday -- a bid Barcelona will not look to match.
"This is getting to be an auction and we will not get involved in that," Laporta said.
Laporta has already missed out on signing England captain David Beckham, who opted instead to join Real Madrid, and the newly elected Barcelona president looks now to have all but given up on making Ronaldinho his big signing for the new season.
"We will only re-open the case if Ronaldinho really wants to come to Barcelona," Laporta said.
Earlier on Wednesday, Manchester United were reported have increased their offer for Ronaldinho to 30 million euros ($33.47 million).
PSG sources were quoted in French sports daily L'Equipe as saying that Barcelona had made a similar bid.
United manager Alex Ferguson said on Tuesday that the English champions were close to landing Ronaldinho, although he expressed caution until any deal was finally done.
