“It is up to the judge Andre Dando to decide whether or not to bring charges against him,” the source told French news agency AFP.
Police also questioned Sydney Govou, another French international who plays for Lyon, AFP reported.
If charged and found guilty Ribery, who represented France in the 2006 World Cup, could face a fine of 45,000 euros and a maximum prison sentence of three years.
On Sunday, Ribery’s lawyer Sophie Bottai said he had been questioned as a witness by police investigating a prostitution case focusing on a Paris nightclub popular amongst French international players.
Judicial sources told AFP that the manager of the club and three others had been charged in the case and were in custody.
“We should not make any declarations while the judicial proceedings are underway,” Bayern Munich’s manager Louis van Gaal said on Monday.
The French Football Federation would not comment.
Ribery is seen as a key player in France’s World Cup line up. After Zinedine Zidane’s retirement, he became a mainstay of the national team and had a successful domestic spell at Marseille.
Recently he has been linked to high-profile transfers to Spain or England, with reported links to Spanish giants Real Madrid.
However, these new allegations against Ribery make any such move unlikely. The Spanish sports daily Marca reported on Tuesday that the scandal had “warded off almost definitely” any chance of him joining the most successful team in Spanish football history.
Although the newspaper cited no official sources, Ribery had said last week that he would make a decision about his future “within 10 days”, and had previously hinted that a move to Spain would be his favoured option.
Ribery helped the German Bundesliga team overturn Manchester United in the Champions League at the start of this month.
And they play French side Lyon in their 13th Champions League semi-final on Wednesday. But Ribery has been pulled from the pre-match press conference to be held in Munich on Tuesday. He will be replaced by German player Philipp Lahm.
Bayern Munich held a meeting with Ribery on Monday.
“Naturally, it is a subject under discussion,” said Christian Nerlinger, the club’s Sporting Director, refusing to give further information.
“We must concentrate on the football, Franck too,” he added.