NFP - run by Jessica Bibliowicz, the daughter of former Citigroup chief Sandy Weill - could be valued at around $1 billion in a deal, the people said on Wednesday, asking not to be named because details of the auction are confidential.

NFP said on March 13 that the company has decided to explore a sale following indications of interest from private equity firms, confirming a Reuters report the previous day.

Representatives for NFP, TPG and Madison Dearborn declined to comment.

National Financial, like many independent brokerage firms, experienced difficulties during the market downturn of 2008 and at one point that year saw its stock hit a low of $1.21 per share.

Its stock closed Wednesday at $22.25 per share.

In February, National Financial reported fourth-quarter net income of $19.4 million, or 45 cents per share, up from $11.2 million, or 27 cents per share, in the year ago quarter.

Total revenue for the fourth quarter grew 3.8 percent to $300.1 million from $289.2 million in the prior year's quarter, beating analysts' estimates.

A sale of National Financial would come almost a year after Bibliowicz stepped down as president of the company in April 2012. The company announced at that time that she would also be stepping down as chief executive at the end of March 2013, at which point she would become non-executive chair. The firm later amended that timeline and she is now scheduled to relinquish the job of CEO in May.

(Reporting by Jessica Toonkel and Greg Roumeliotis in New York, Editing by Soyoung Kim and Steve Orlofsky)

By Jessica Toonkel and Greg Roumeliotis