The New York Post reports that Facebook is only willing to sell more shares in the company if it gets a valuation in the region of $5bn to $6bn.
However, the newspaper, which is part News Corporation, owner of MySpace, says that offers only value Facebook at around $2bn to $3bn.
The newspaper claims that sources said Facebook is in talks with potential investors including private equity firms Kohlberg Kravis Roberts and General Atlantic.
In October 2007, Microsoft bought a 1.6% stake in Facebook for $240m. It was at the height of the website's growth.
The site remains hugely popular, but with the company in private hands its revenue and profitability remain unknown.