The American owners announced on Tuesday they were looking to "explore strategic alternatives".
The move follows years of protest from fans since the Glazers bought the club for £790m ($1.34bn) in 2005.
"This is good news," said Manchester United Supporters' Trust (Must) communications director Chris Rumfitt.
"It very much looks like they have hung up the 'for sale' sign around the decaying gates of Old Trafford.
"Every Manchester United fan has woken up with a bit more of a spring in their step this morning."
The club's announcement said the board would "consider all strategic alternatives, including new investment into the club, a sale, or other transactions involving the company".
It added the process "will include an assessment of several initiatives to strengthen the club".Rumfitt said Must would be seeking an immediate clarification of the Glazer family's intentions.
Speaking to BBC Radio 4's Today programme, he added: "If that [selling the club] is not their intention, they need to clear that up pretty quickly and they haven't done so."
Must later released a statement saying the club needed "new investment more than ever".
It said United fans had become "dismayed with the ownership of the club" amid a "decline on the playing side and a decline in our stadium".
"Any prospective new owner or investor has to be committed to the culture, ethos and best traditions of the club," it said.
"They have to be willing to invest to restore United to former glories, and that investment must be real new money spent on the playing side and the stadium."
Must also said any new ownership structure "must embed supporters, including a degree of fan share ownership, in their operating model".
It added: "Manchester United's fans are its greatest asset and hold the key to unlocking the true value of any football club. That relationship has to be one of equals - sharing in ownership and unified with the same goals."
In 2012, the Glazers sold 10% of their holding via a stock listing and have sold further shares in the subsequent years.