The Manchester United Supporters' Trust says the two bids made for the club have raised questions about sporting integrity, debt levels and inclusivity.
Sheikh Jassim bin Hamad Al Thani, chairman of one of Qatar's biggest banks, has also tabled a bid.
MUST has a "clear list" of demands for owners, but add "further considerations arise" with the two official bids.
The Glazer family, who have owned United since 2005, are considering selling the club and a 'soft deadline' of Friday was set for proposals.
The American owners confirmed they wanted to "explore strategic alternatives" for the club.