The Princess Anne and The Princess Margaret have been at risk since the government’s Homes and Communities Agency (HCA) seized ownership of them nine years ago.
They had been promised to the museum by the original owners, Hoverspeed, but the deal fell through – after they had already been moved on the HMS Daedalus site in Lee-on-the-Solent.
A campaign began to save them from being sold off by the HCA – which owns the museum site – and it now looks as if an agreement has been made.
Warwick Jacobs, one of the trustees, said: ‘We have not heard directly from the HCA but we are cautiously optimistic that we are very close.
‘While we’re excited about the prospect we haven’t actually been told yet.
‘And although nothing has been signed yet, we’re optimistic that we’re coming to a positive conclusion. It’s taken a long time to get to this stage.’
Mr Jacobs said the only down side is parts from the Princess Margaret – which is in bad condition – will have to be used to complete Princess Anne.
Speaking to the BBC, a spokesman for the HCA said it was in the process of agreeing a lease for the Princess Anne with the Hovercraft Museum.
HCA said it would consider options for the second hovercraft, The Princess Margaret, which is understood to be in a worse state of repair, once the lease for The Princess Anne was complete.
Museum volunteers started a petition to save the hovercraft in January after HCA announced it wanted to develop the land for homes.