A takeover battle between the bus tycoon brothers and billionaire Jim McColl was under way to take control of the Port Glasgow yard, which went into administration last week, putting 77 workers out of a job.
Engineering tycoon Mr McColl, who saved about 550 jobs at Weir Pumps in Glasgow in 2007, is now front-runner to save the yard.
The Easdales pulled out after a conversation with Mr McColl yesterday.
Mr McColl has promised to invest "many millions" of pounds in Ferguson if his offer is accepted.
A spokesman for the duo said: "The Easdale brothers are delighted that a businessman with Jim McColl's engineering background is keen to take over the yard.
"Sandy spoke to Jim at length this morning, and his plans for hundreds of jobs and millions of pounds in investment are exactly what Inverclyde needs.
"We are informed our bid is competitive and has reached the shortlist.
"But we feel Jim McColl is better equipped to take the yard forward.
"We said all along we would step aside if somebody with an engineering pedigree and access to markets wanted to get involved.
"Our only interest has been to save the yard and as many jobs as possible.
"As local businessmen, the Easdales have a strong interest in seeing a thriving Inverclyde economy."
First Minister Alex Salmond has met the workers who lost their jobs and held private talks with joint administrators Blair Nimmo and Tony Friar, of accountancy firm KPMG.
After the hour-long meeting, Mr Salmond said: "I have great hopes the work undertaken in this century-old yard will continue under new ownership."
Administrators will now evaluate the three remaining bids and hope to select a preferred bidder early next week.