The owner of Madame Tussauds, Merlin Entertainments Group, is believed to be in final preparations for a £2bn London Stock Exchange listing early next year.
Such a substantial offer of shares could see the firm instantly projected into the FTSE 100.
Merlin is currently owned by the US-based private equity group Blackstone.
The investment banks Goldman Sachs, JP Morgan Cazenove, Citi, Merrill Lynch, Deutsche and BNP Paribas have all been involved over the last few months in a bid to be advisers to the projected flotation.
In July, Merlin's chief executive, Nick Varney, said: "If a flotation is going to happen, then the markets have to be open – and at the moment they're not." He added: "Merlin would be a very strong and popular listing but I can't say at the moment if we're going to float."
The recent stock market rally has made Merlin and Blackstone think about bringing forward the tentative plans for listing early next year.
Merlin was originally known as Vardon Attractions, which owned the Sea Life Centres, and has expanded to become the world's second biggest entertainment group after Disney. Warwick Castle, Legoland and the London Eye are among the other attractions to have become part of Merlin.
There are suggestions that Blackstone could include Center Parcs, the resorts group acquired in 2006, in the Merlin listing.