The firm, which maintains and upgrades three London Underground lines, was supposed to complete upgrade work on the Jubilee Line by the end of next month.
But it has admitted it will miss the deadline because it needs six more weekends of closures to complete the work.
Transport for London (TfL) boss Richard Parry said earlier this year that the company's desire for more weekend closures "has stretched stakeholder and customer patience to breaking point.
"It is vital that Tube Lines meet their commitment to deliver the upgrade by 31 December 2009. Their reputation – and that of their shareholder Bechtel who is delivering this project – hinges on meeting this commitment."
Dean Finch, Tube Lines chief executive, told the Daily Telegraph that the fines would be "painful", but, "Tube Lines will bear the pain – not the taxpayer."
He added: "It’s very big concern for Tube Lines, but I don’t think it will kill it. We will have to juggle our programme very carefully. Hopefully, we will reduce these costs over time."
A Tube Lines spokesperson said the company was in negotiations with London Underground over 2010 closures. "Whatever London Underground agree will dictate when we will complete the project."
He added that the dispute would not affect negotiations over the cost of the next seven years of upgrade work from 2010.
These discussions have also been fraught, with TfL and Tube Lines billions of pounds apart on how much the work should cost. The PPP Arbiter, who has been called in to settle the disagreement, will make his final decision by next April.