But Barcelona finished third in La Liga this season and were knocked out of the Champions League at the semi-final stage during a trophyless campaign.
Laporta is now instigating major changes and has already ended Rijkaard's reign, with the Dutchman being replaced by Pep Guardiola for next season.
Rijkaard and Ronaldinho, who both joined Barca in 2003, helped the club clinch the league title in 2005 - the first since 1999 - and then the Champions League and la Liga double the following year.
Laporta added: "I very much hope that Ronaldinho can leave as Frank Rijkaard has done, with his head held high, and that we can remember him as the man who gave us two League titles and one Champions League title.
"I am very grateful to Ronaldinho."
Mourinho not coming is not a decision taken by Cruyff
Barca president Joan Laporta
Barcelona striker Samuel Eto'o has also been linked to a move away from the Nou Camp and Inter Milan and Tottenham appear keen on the Cameroon international.
Laporta stated: "Eto'o is a player who is loyal to the colours, who sacrifices himself, who people like.
"The day he goes he deserves a big send-off and to leave with full honours."
Meanwhile, Laporta denied the club took the decision not to go for Jose Mourinho as manager on the advice of Barcelona legend Johan Cruyff.
"Mourinho not coming is not a decision taken by Cruyff," insisted Laporta.
"I asked him what he thought, as I ask lots of people. In this case, Cruyff is very much in favour of Pep Guardiola."
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