It was originally due to expire at the end of this month but the government has the power to extend it as far as October next year.
President Barack Obama and Treasury secretary Timothy Geithner are thought to have now decided to take up this course of action.
Official have said that the focus of the program will shift away from bailing out big banks on Wall Street and move towards a greater concentration on helping homeowners secure mortgages and freeing up credit for small business, reports Reuters.
The cost of TARP was originally pencilled in at $700 billion but officials say the White House is now prepared to commit to spending no more than $560 billion on the scheme.
Last week, Mr Geithner told Congress that shutting down the initiative completely would be a mistake.
"If you look at the US financial system today, there are parts that are still very damaged," he stated.
President Obama has also defended TARP against Republican attacks describing it as no more than a "slush fund" being used by the White House for job creation.
"There has rarely been a less loved or more necessary emergency program than TARP, which as galling as the assistance to banks may have been, indisputably helped prevent a collapse of the entire financial system," he said this week.
Last week, Bank of America announced its plan to exit TARP as soon as possible by fully repaying its $45 billion debt to the government.
It will raise the necessary fund by selling $18.8 billion worth of securities and using $26.2 billion in excess assets.
Bank of America estimates the move will save it around $3.6 billion a year in interest on its repayments.
By Asim Shah