According to a report in The New York Times details of the settlement have not been disclosed, but a deal could be done "within weeks", according to a source quoted by the paper.
The source, who has been briefed on the settlement negotiations, did not divulge any proposed terms of the agreement.
The lawsuit was brought by brothers Cameron and Tyler Winklevoss and Divya Narendra who claim that Facebook's founder Mark Zuckerberg stole their idea after they hired him as a programmer to help set up a university dating site called Harvard Connection.
They claim Zuckerberg delayed their project and stole their source code and business plan. They say that he went on to use this to launch Facebook in 2004 as a social networking site for students.
The three subsequently launched , which offers a similar kind of service to Facebook, but it has not enjoyed anything like the phenomenal success of Facebook.
The claimants filed the suit in the middle of last year, alleging copyright infringement, stealing trade secrets, fraud and breach of contract. Zuckerberg filed a counter suit of defamation. A federal judge ordered the parties into mediation last year.
While the case has caused public relations problems for , the social networking site continues to increase its unique users figures and claims to have almost 70m users worldwide.
Facebook needs to get the case out of the way if it is to float part of the company, which has been valued at $15bn.
However, with the market jittery and social networking continuing to fragment, Facebook needs to move quickly to ensure that it does not miss its window of opportunity.