The Red Knights, a group involving former Football League chairman Keith Harris and Goldman Sachs chief economist Jim O'Neill, said on Wednesday they would not be making a bid for the time being.
Last week the Glazer family, who own United, said they had no intention of selling.
"The Red Knights remain committed to pursuing their efforts to try to help bring ownership of Manchester United to its supporters and under a structure with materially less debt," the group said in a statement.
"As we have maintained however since news of our ambitions first emerged in March, we will only attempt to purchase the club at a sensible price, consistent with the long-term interests of the club," the Red Knights added.
"Persistent speculation in the media of inflated valuation aspirations has made our goals less attainable, as potential investors have strongly reinforced our views we should not move forward at a price uneconomic for the future of the club.
BID REJECTED
"We have spent some considerable time assessing the value of the club. If the fundamentals lead to a more realistic re-assessment then ... we will aim to achieve our goals."
A source close to the matter who declined to be identified told Reuters last month the Glazer family rejected an offer of about 1.5 billion pounds ($2.20 billion) from a Middle East investor in 2009.
In a separate statement on Wednesday, the Manchester United Supporters Trust said they "completely support the stance of the Red Knights group not to pay a ridiculous premium price to the Glazers."
The Glazer family of sports tycoons bought United for about 790 million pounds in 2005 against a wave of opposition from fans. The club's debts have since swelled to about 716.5 million pounds.
