Harris, the head of merchant bank Seymour Pierce, has been involved in four Premier League club takeovers and has long been critical of United's debt that earlier in January was recorded at £716m.
United's recent bond issue raised £500m to ease their debts, but also provoked a furious backlash from many fans, some demanding an immediate change of ownership.
Despite the move by the Manchester United's Supporters' Trust, the Glazer family have told BBC Sport that they are here for the long-term and insisted that their interests are aligned with those of the fans.
On Friday members of Manchester United's Supporters' Trust met with "super-rich" and "influential" investors, with lifelong United fan Harris at the centre of the discussions.
Harris declined to name any of the people who have approached him, identifying them only as 'The Red Knights'.
"We have been approached and if we can lend our weight for doing something for the good of Manchester United and football we will," Harris told BBC Sport's Football Focus show.
"In this case of Manchester United, of whom I am a huge fan and have been for 50 years, they are playing with an icon of football, one of the most respected football brands in the world and it is in danger.
"Seventy-five pence of every pound that [Manchester United] fans are spending is now going to the Glazers either for themselves or to pay debts."
Senior members of the Manchester United Supporters' Trust met with the 'Red Knights' on Friday in London
BBC Sport's Dan Roan
"If these rumblings become a revolution and fans stop going - as difficult as it is for them not to go - and the pounds stop coming in, there is real peril."
Malcolm Glazer and other members of his family took control of Manchester United in 2005 but their purchase of the club was largely funded with borrowed money.
Interest payments on that money have since plunged United into deeper debt and despite winning the Premier League for the third year in a row, the Carling Cup and the Club World Cup last season only the £80m sale of Cristiano Ronaldo to Real Madrid helped the club record pre-tax profits of £48.2m for the year to 30 June 2009.
The team also finished runners-up in the Uefa Champions League.
Harris is unsure how the offer will be received by the Glazers but believes the family should in effect take the money and hand over the keys to Manchester United.
"It depends on the Glazers' attitude," added Harris.
"Clearly they appeared impervious to the protests when they took the club over and that was fine.
"They don't go [to watch United] very often, they stay in America but you've got to think their businesses in America haven't done well, they can't have done, because the world in general has not done well in business.
"They are probably highly geared in their business activities in America so, if this is an opportunity for them to take the money and go, I would hope they would listen carefully to that offer, providing the money can be raised and I am confident it can be."
But Manchester United themselves have told BBC Sport that they are comfortable with the financial situation at the club, and that manager Sir Alex Ferguson has the £80m the club received from Real Madrid for Ronaldo to spend on new players.
"Manchester United is the most profitable football club in the world," read a club statement.
"Last year, on a record turnover of £278m, the club made a record cash profit of £91m. Interest payments were £41m and wages accounted for less than half of the turnover.
The Glazer family, led by Malcolm Glazer, bought United in 2005
"The recent bond issue has been very successful and provides the club with certainty in its interest payments, as well as great flexibility with the removal of bank covenants.
"The cash from the sale of Cristiano Ronaldo is available for Sir Alex to spend and it will be spent on players who are available for purchase and who the manager thinks can improve the squad, not to prove to pundits that it exists."
Harris is unsure how much a takeover will cost, but is certain that the time has come for change at Old Trafford.
"It's too early to say how much would have to be raised," said Harris.
"These debts have run on for a long while and I think they need to be cleared.
"I would hope that there would be sufficient money in addition to that to show the Glazers they could take a profit for owning the business for five years and go and put the ownership into more caring hands.
"This is now serious, what you don't know is if the Glazers can be made to listen, but what you do know is that there is a serious intent on the part of those people, who have not just support in their hearts, but the ability to muster support from their pockets to get after this, and the time feels right."
Interviews by BBC Sport reporter Dan Roan. Writing by broadcast journalist Nabil Hassan
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