The trustees of the foundation have not yet agreed to take control of the club.
The billionaire, who would remain the club's owner, made the move during the Russian invasion of Ukraine.
On Sunday, members of the charitable foundation met to discuss the situation.
The foundation's lawyers are looking into what can be done after some people had concerns about whether the charity commission rules would allow them to run the club.
Some members of the foundation are concerned about their legal liability if they agree to run the club.
The announcement was made on the eve of the Carabao Cup final.
"I have always taken decisions with the club's best interest at heart."
I remain committed to these values. I am giving the trustees of the Foundation stewardship and care of the club.
I believe that they are in the best position to look after the interests of the club, players, staff, and fans.
The situation in Ukraine was "horrific and devastating", according to a statement released on Sunday.
Everyone in Ukraine has the thoughts ofChelsea FC. The west London club said that everyone is praying for peace.
The trust said it was seeking urgent clarification on what the statement on Saturday means for the club.
The UK Government has taken measures against Russia, but it is not known if it will include sanctions against Abramovich.
The owner of the club gave them a loan but it is not being called in.
One of Russia's richest people is believed to be close to Putin.
The community and education departments are run by the foundation. Bruce Buck is the chairman of the club as a whole.
The other trustees of the foundation are Sir Hugh Robertson, Piara Powar, and John Devine.
The club have won the League Cup three times, the FA Cup five times, the Europa League twice, and the European Championship twice.
Chris Bryant, a Labour member of the House of Commons, said he had a leaked Home Office document that suggested that Roman Abramovich should not base himself in the UK. He wants the government to take his assets.
Unless and until he condemns the criminal invasion of Ukraine, I will continue to call for the UK to sanction him and seize/freeze assets.
There were claims made in the House of Commons.
The trust said it was ready to work with the trustees of the foundation to ensure the long-term interests of the club and supporters.
We stand with the people of Ukraine.