He said Manchester United's Supporters Trust had held meetings with influential supporters who were interested in investigating a change of ownership and ending the huge debt strategy employed by the current American owners, the Glazer family.
Harris, the head of merchant bank Seymour Pierce, is a lifelong United fan and has been involved in four Premier League club takeovers.
He has been a staunch critic of United's debt which last week was revealed to be 716 million pounds.
Harris told the BBC's Football Focus programme on Saturday: "You sense that the momentum is gathering and this time these fans truly mean it. I think they are saying that enough is enough, there is too much gearing on this football club and it is unhealthy.
"We have been approached. We can lend our weight to doing something for the good of United and for the good of football - none of the takeovers that I have been involved in have involved any debt.
"They've been takeovers by people who've wanted to be involved for reasons other than money."
Harris would only identify those involved as 'The Red Knights', adding: "A number of people have been to see me and I've had long chats with them. There are one or two people in senior positions in the financial services that have access to capital.
"We don't know if the Glazers can be made to listen, but there is serious intent on the part of people who have support in their hearts. The time feels right."
Earlier this month United's owners issued 500 million pounds' worth of bonds in a re-financing effort.
He added: "(The Glazers) are playing with an icon of football, one of the most respected brands in the world, and it is in danger," he said.
"Seventy-five pence of every pound fans are spending is now going to the Glazers either for themselves or to pay debts."
United issued a statement denying there were problems, saying: the club was the "most profitable football club in the world."
