Before being accused of sexually assaulting a hotel maid in New York on 14 May, Mr Strauss-Kahn was tipped as a possible French presidential candidate.
But doubts have since emerged about the credibility of the maid, and the case is reportedly close to collapse.
On Friday a judge ordered Mr Strauss-Kahn released on his own recognisance.
His is now free to travel in the US, although he cannot leave the country and must appear in court again later this month.
Mr Strauss-Kahn, who resigned as head of the International Monetary Fund to defend himself, vigorously denies the charges.
DeadlineMr Strauss-Kahn had earlier been the favourite to be the Socialist Party's candidate for the French presidency in May 2011.
The BBC's Christian Fraser in Paris says that regardless of events in court, the expectation is growing here in France the case will ultimately collapse.
And if that happens, the only person who can rule his out of next year's contest is Mr Strauss-Kahn himself, our correspondent adds.
Continue reading the main storyHere in Paris there is huge anticipation. The man who had been written out of the script for next year's presidential elections is potentially back in the running.”End Quote
Gavin Hewitt BBC Europe editor The last Socialist Prime Minister, Lionel Jospin, said: "If we hypothesise that Dominique is cleared of all suspicion and all charges, which I obviously hope will happen, then it will be first down to him to decide... and then it will be down to the Socialists to decide."A Socialist MP, Jean-Marie Le Guen, said he thought it likely that Mr Strauss-Kahn would stand.
"Yes, he will be present for the presidential campaign," he said.
"If what we heard... is true, that the American justice will free him and re-habilitate him, give him back his honour and dignity. Then, since Dominique Strauss-Kahn is a fighter, he will fight in our country."
The list for nominations is due to close on 13 July - five days before his next scheduled court appearance. But the senior Socialist, Francois Hollande, said the deadline could be extended.
Our correspondent says there are though plenty in France who hold Mr Strauss-Kahn in high admiration for the way he has conducted himself in court, there is sympathy and renewed hope among his staunchest allies.
'Lie'A judge in New York lifted the strict bail conditions imposed on Mr Strauss-Kahn, amid intense speculation that the sexual assault case against him was faltering.
He had been under house arrest since posting a $6m bail bond.
When the 62-year-old appeared in court, prosecutors were forced to admit that they were reassessing the strength of the evidence against him - although the charges that he attempted to rape a hotel maid still stand.
In a letter submitted to the court, the prosecutors said that the maid had given false testimony to a grand jury, omitting the fact that she had cleaned another room before alerting a supervisor to her claims of sexual assault.
Manhattan District Attorney Cyrus R Vance Jr: “Our office's commitment is to the truth and to the facts""I understand that the circumstances of this case have changed substantially, and I agree the risk that he would not be here has receded quite a bit. I release Mr Strauss-Kahn at his own recognisance," Justice Michael Obus told the court.
The maid claims that Mr Strauss-Kahn chased her down a hallway in his expensive hotel suite in the Sofitel hotel before sexually assaulting her.
However, unnamed law enforcement officials have now told US media the accuser has repeatedly lied since the alleged attack.
The officials believe the woman also lied on her application for asylum, particularly over an allegation that she had been raped while at home in Guinea. They also suspect she has links to drugs dealers and money-laundering.
Mr Strauss-Kahn's lawyer, William Taylor, said he believed the next step would lead to the complete dismissal of the charges.
But the maid's lawyer, Kenneth Thompson, maintained that his client's story was genuine and that Mr Strauss-Kahn was guilty of sexual assault charges.
"From day one she has described a violent sexual assault that Dominique Strauss-Kahn committed against her," Mr Thompson said, adding that Mr Strauss-Kahn bruised the maid's body and threw her to the floor.
"She has never once changed a single thing about that account. The district attorney knows that," he added. "The only defence Dominique Strauss-Kahn has is that this sexual encounter was consensual. That is a lie."
