The Cutty Sark Trust has been awarded £1.3m of lottery funding and a further £11.7m has been earmarked to help save the historic ship in south-east London.
The lottery money will cover part of the ship's £25m restoration plan
The Grade I listed attraction, which is decaying, will be restored and turned into a maritime heritage centre of excellence in Greenwich.
In November, the trust said it would have to close the 143-year-old ship as an attraction without the grant.
The Heritage Lottery Fund has so far donated about £500,000 to the vessel.
The trust now needs to make a second, more detailed application, to finalise the larger donation.
The combined grants would help to pay for more than half of the £25m needed to save the ship.
The architects Grimshaw, who designed the Eden Project in Cornwall, are working with the trust to develop the plan.
This includes raising the ship up in her dry berth so visitors can walk underneath and see the ship's conservation. Some of her sails would also be reinstated.
Richard Doughty, chief executive of the Cutty Sark Trust, said: "The Heritage Lottery Fund has effectively saved the ship.
"This groundbreaking project will not only conserve the fabric of the ship, but will also ensure she retains her status as a world class visitor attraction."
Carole Souter, director of the Heritage Lottery Fund, said the move was a "wonderful use of lottery players' money".
If all the funding can be secured then work on the ship is due to begin next year.
The Cutty Sark - the world's only surviving tea clipper - was originally used to deliver tea from China and later collected wool from Australia.