The brothers described the Ferguson shipyard as the "last bastion of the ship industry in the whole of Inverclyde" and said they had a moral obligation to explore rescuing the business to ensure vital skills were not "lost forever".
The Greenock-based Easdales, who own McGill's Buses, are today set to meet with administrators KPMG, which has blamed cashflow pressure and a lack of orders for the company going bust. The pair have assembled an expert team that will examine the strength of the shipyard.
Sandy, 46, said: "It's very early days. But we've put ourselves forward and expressed an interest so that we can have a look at it. We feel an obligation to try and keep an industry that we were brought up in going.
"The Inverclyde area, for hundreds of years, was identified with shipbuilding in the lower Clyde. When I was growing up as a boy, the shipyards stretched about 15 miles. We're not promising anything at this moment in time. What we're saying is we'll have a look, and if it's viable we'll have a go at it."
James, 43, added: "It's too early to paint ourselves as saviours but we are looking at it. We're yet to meet the administrators.
"Once we go there we'll know whether we're opening Pandora's box or if there's something viable."
Previously, the brothers have rescued local window firm Blairs, which had hit hard times during the recession. Although its workforce had been made redundant when they took the crisis-hit company over, its fortunes were turned around and it currently has 70 employees.
Sandy said Government support would be vital if any takeover was to succeed.
While Ferguson's has built two ferries for the Scottish Government-owned firm CalMac in the past three years as part of a £20 million contract, some work has gone overseas as a result of EU procurement rules.
He added: "We may not be the best choice - we're not shipbuilders. If there's a second choice there, we'll stand aside and let those guys get on with it. To save the industry is the most important thing. What local government and national government can do is come forward and cut the red tape for this yard to survive.
"Procurement at national level, when work goes to foreign countries, or goes into Europe, is the biggest problem. The Scottish Government, or the UK Government, will need to say 'enough's enough, the ships are built in Scotland for the Scottish workforce'. They've got to address a situation where we have foreign shipyards taking our jobs in the EU market."
Only seven of a 77-strong workforce at Port Glasgow-based Ferguson's have been retained as a skeleton staff while a buyer is sought. A task force, convened by the Scottish Government to explore new opportunities for the shipyard, met yesterday. After the meeting, Finance Secretary John Swinney pledged to do everything in his power to ensure Ferguson's had a future. The Scottish Government has been informed of the Easdales' interest.
Jim Moohan, GMB Scotland senior organiser and chairman of the Confederation of Shipbuilding and Engineering Unions, described talks with the Scottish Government as constructive but said it was vital there were meaningful developments within days. He added: "Every employee left the yard on Friday without a penny after 35 to 40 years' service, which in itself is a scandal.
"We told the Finance Secretary that there is still limited work within the yard which can be progressed alongside work that was being done on the conversion of a ship nearby. We also raised the importance of two further CalMac hybrid ferries, which we believe could secure the future of the shipbuilding yard."