The former Barcelona and AC Milan forward was among 16 players who left for next week's match away to Real Potosi, who, at 4,070 metres above sea level, are believed to have the world's highest first division stadium.
Reports in local media say Ronaldinho is owed 3.75 million Brazilian reais ($2.1 million) by the sports marketing firm Traffic who pay part of the former FIFA World Player of the Year's salary.
The club said they were counting on Ronaldinho, who joined Flamengo from AC Milan a year ago, to play in the first leg of the preliminary round tie.
"We are not working with the possibility of him not playing," club president Patricia Amorim said at Flamengo headquarters.
"It looks like things will be sorted out. We're giving Traffic options with a view to a happy ending," she told a news conference shortly after the team's departure.
Ronaldinho's brother and agent Roberto Assis told media he had reached a deal with the club and Traffic with the promise that the debt would be paid on Wednesday.
He said Ronaldinho had only boarded the plane to Bolivia after that promise was made, adding there were no guarantees over the player's future at the club.
"Flamengo came here, we had a meeting, we talked quite a lot about the situation and the club has until Wednesday to take a stance and come to an agreement with Traffic," Assis told the Globo sports website.
"Nothing has been settled yet. Flamengo said they would do all they could to resolve the problem. I believe it's in no-one's interest to carry on like this," he added.
Flamengo, who will spend a week acclimatising in Sucre at 2,800 metres before their match in the famous mining town of Potosi on January 25, may have managed to take Ronaldinho with them but appear to have lost central defender Alex Silva.
Silva, a former Brazil international, did not show up at the airport and was immediately suspended by Amorim.
"Alex Silva gave us a surprise. We're not sure exactly what it's about, whether it's a financial problem... he has been separated [from the team], this is a serious breach [of discipline]. The case is with our judicial department," she said.
