A list of promises has been outlined by the family if they win the bid to buy the club.
The Chicago Cubs owners were included on the list of potential buyers of the west London club, but came under pressure from the CST, who said that 75% of its members do not support their bid.
Over the past couple of weeks, the Ricketts met with several supporters of the club and listened to what they had to say.
As we enter the next phase of the process, we are sharing a list of specific commitments that give fans a pivotal role in protecting the heritage and building for future success, they said in a statement on Sunday.
We will discuss our ambitions for the club with fans and the wider football community in the coming days.
The CST does not have a seat on the board or the power to veto its decisions, which is why it is seeking more influence at the club. The family said the CST would be on an advisory committee.
The advisory committee would have a former men's and women's first team player, members of the pitch owners and influential community leaders.
Other commitments include investing in the first team and academy to continue winning trophies, and ensuring the women's team also plays matches at Stamford Bridge.
Roman Abramovich put the club up for sale before the British government imposed sanctions on him, giving him control of the club.
The winning bidder must also be approved by the government as the U.S. Bank Raine Group is overseeing the sale.