The Glazers, who bought United for 790 million pounds in 2005, are selling 8 million of their shares in the club which amounts to a stake of about five percent.
Once the shares are sold, the six children of the late Malcolm Glazer will still own more than 80 percent of the club's total shareholding.
None of the proceeds will go to the club itself, a fact that is likely to annoy some fans who have long campaigned against owners they accuse of burdening United with excess levels of debt following their takeover.
The sale of the shares would create a more liquid market for United stock after a flotation on the New York Stock Exchange two years ago.
The shares were listed at $14 and have risen to a price of $19.31 on Wednesday, valuing the club at almost $3.2 billion.
United, English soccer champions a record 20 times, are seeking to rebound after a poor season in which they finished only seventh in the Premier League, missing out on a place in lucrative European club competition in the coming season.
Optimism has been fuelled by the arrival of a new team manager, Dutchman Louis van Gaal, and the signing of a new sports equipment deal with Adidas worth a record 750 million pounds over 10 years. General Motors Co made a $559 million seven-year sponsorship deal with the club for GM's global mainstream auto brand, Chevrolet, to appear on team jerseys.
The Glazers also own the NFL team The Tampa Bay Buccaneers. Family patriarch Malcolm Glazer died earlier this year.
The book-running managers for the share offering are Jefferies, BofA Merrill Lynch, Credit Suisse, Deutsche Bank and Nomura.
(Editing by Grant McCool)
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