Smith New Court has said that it is in discussions with possible bidders and would like to do a deal. So far Merrill Lynch, the US investment bank, and Commerzbank, the German bank, are the front-runners.
Sir Evelyn, whose bank holds the largest and most critical shareholding in the stockbroker, is insisting that if he is to give his agreement to a sale, a bidder for Smith either retains the existing arrangements or pays a significant premium to NM Rothschild, perhaps up to pounds 50m, in compensation for their loss.
Neither Smith New Court nor NM Rothschild yesterday would detail precisely what arrangements existed. Sources suggested that whatever arrangements there were - an option on tie-ups between the two on certain corporate finance deals, for example - suited NM Rothschild rather more than they suited Smith New Court.
Both Merrill Lynch and Commerzbank have indicated in discussions that they would be prepared to pay at least 550p a share for control of the stockbroking house. That would leave NM Rothschild with an exit price of around pounds 100m for its shareholding. On top of that Sir Evelyn is looking for a substantial sum, perhaps as high as pounds 50m, in compensation.
One problem for NM Rothschild is that the sale of its shareholding in Smith New Court, first acquired in December 1983, will undoubtedly raise questions about its own strategy.
"Everybody else seems to be linked with a parent. There must be a danger of Rothschild, especially if it loses its equity distribution link, being left out of the large corporate deals in the future," says David Poutney, an analyst at stockbrokers Collins Stewart.
Others were sceptical about the value of the tie-up between the two firms. "I think that the Smith New Court people found it hard to put their hearts and minds into the idea that they were a partnership with NM Rothschild," a senior corporate financier said.
"I think they felt that Rothschild turned their noses up at them and found greater affinity with the people at Cazenove or Warburg," he added.
Michael Marks, the Smith New Court chairman, is believed to strongly favour a tie-up with Merrill Lynch.