The Chelsea Supporters' Trust (CST) said on Saturday that 77% of its members do not support the Ricketts family's bid for the Premier League club, in the wake of a fan backlash over previous racist remarks by members of the family.
The announcement comes on the same day a small group of fans staged a protest outside Stamford Bridge against the Ricketts bid ahead of Chelsea's clash with Brentford.
The Ricketts, who own the Chicago Cubs baseball team, have been included on the shortlist to buy the London club.
CST, which is seeking greater influence at the club but does not have a seat on its board or the power to veto its decisions, said this week that the family should show how it would address supporter concerns with regard to inclusivity.
On Saturday it said a survey of its members showed more than three-quarters oppose the Ricketts' bid and 72% do not have confidence that the family would run an inclusive club.
"It is essential that the new owners of Chelsea FC have the confidence of the supporter base and demonstrate an understanding of the values that we stand for," CST said in a statement.
"At present, it is clear that our membership neither supports nor has confidence in the Ricketts family's bid for the club."
In response, the family reiterated that it was committed to inclusivity and had met many Chelsea fan groups and that if its bid goes through it was ready to make a range of commitments to the club and fans.
"We believe these are far-reaching and certainly include an absolute commitment on the part of the Ricketts Family and the bid team to put diversity and inclusion at the heart of the club," it said. It made similar comments in a statement on March 23.
"We look forward to more meetings -- including with the Chelsea Supporters' Trust -- over the coming days and to making a public reiteration of our values and commitments," it added on Saturday.
CST said they would survey their members again if the Ricketts family "publicly set out clear and detailed plans on how they will address support concerns".
Outside Stamford Bridge on Saturday, a small number of Chelsea fans held "No to Ricketts" signs to demonstrate against the family's bid.
Chelsea were put up for sale by Russian billionaire Roman Abramovich before sanctions were imposed on the oligarch by the British government, effectively giving it control of the club.
U.S. Bank Raine Group is overseeing the sale and the winning bidder must also be approved by the government.