The website's loss in value coincided with the entrance to the market of competitors such as Tesco's Tescocompare.com, and the prominence of rivals including Confused.com.
While shares in Moneysupermarket have begun to rise after news of the private equity approach became public, rising 22% to 84.25p, the share price is still considerably lower than their 170p value when the company was floated in August 2007.
More than half the company is owned by chief executive Simon Nixon.
Last July, the company was forced to issue a profits warning and shares fell 30% in value. The warning followed an announcement by Barclays Bank that it was to close its secured loans arm, FirstPlus.
Moneysupermarket.com earns commission from the products to which users sign up, and the closure of the Barclays unit is thought to have cut the comparison site's revenues by £7m and Ebitda by up to £5m.
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