Mr Goldsmith's company, Allied Entertainments, wants to buy the former Victorian train shed and revive it as a multi-purpose venue seating 2,500 people.
A plan shown to English Heritage's London Advisory Committee this month involved an elaborate mechanical structure that would enable three of the 26 internal columns to be removed so that the circular venue could be used either for theatre in the round or with a traditional proscenium. It would also stage sporting contests, such as boxing, and circus events.
But English Heritage has said none of the columns can be removed in the building, which has not been used for the past 11 years.
However, the views of English Heritage officers and the London committee are known to be at odds with those of the chairman, Jocelyn Stevens, who is keen to see the Roundhouse in use again.
Last year, Camden council sold the venue to Keatway Leisure for pounds 895,000 on condition that pounds 400,000 was spent clearing asbestos waste on an adjacent site. The company now appears to be willing to sell it on.
Allied Entertainments director Edward Simons said: 'Anybody who loves this building wants to see it operative. We believe in the building. I took a decision to spend money in developing a scheme but we are not about to spend millions of pounds without the blessing of English Heritage.'