The fundraising project was launched six months ago but now stands at £84,350, and the organisers hope to have raised £100,000 by the end of December.
The 60-year-old vessel is the last paddle steamer to have been built in Britain.
Despite not having sailed in more than three decades, it is a popular tourist destination at its berth at Balloch, Loch Lomond. Hundreds of visitors were attracted to it over the summer.
A few weeks ago, actors Timothy West and Prunella Scales, long-term supporters of the Maid, went on board and said they would love to sail on the Maid should the appeal meet its target.
Mr West said: "We would sail on it at the first available moment. It's something that will happen - I just hope I live long enough."
Phil Preston, chairman of the Loch Lomond Steamship Company, the charity that owns the boat, described the raising of more than £80,000 as "wonderful".
He added: "We are all delighted with this support for the Maid and, although there is a long way to go, we have made good progress. We thank everyone who has helped so far. Donations have been received from all over the UK."
Further fundraising events are planned, including an exhibition of artwork on board at the end of the month, and there are plans for a gala dinner next March at the Cameron House Hotel, beside Loch Lomond.
Mr Preston said the dinner would celebrate the end of the first year of fundraising.