"A group of high net worth individuals, who support Manchester United, met in London yesterday [Monday]," the Red Knights said in a statement.
"This group is supportive of current management, but are looking at the feasibility of putting together a proposal to be put to the Glazer family regarding the ownership of Manchester United."
The discussions, which are in their early stages, are being led by Keith Harris, a football deal broker and the chairman of investment bankers Seymour Pierce, and Jim O'Neill, chief economist at Goldman Sachs.
The group's statement said they saw the Manchester United Supporters Trust (Must) as the a key to success in their takeover attempts.
The United supporters group has stepped up its campaign in recent week to force the Glazers out of Old Trafford, notably by getting fans to wear green and gold - the colours of Newton Heath, the club's original name.
Duncan Drasdo, the Must chief executive, said on Tuesday: "Initially the Red Knight Group has effectively set a challenge to Manchester United supporters to demonstrate they wish to see an alternative ownership proposal developed.
"In the first instance supporters are being asked to do this simply by joining the free online membership of the Supporters Trust and swelling its ranks to an initial target of at least 100,000 [members]."