Mr Sugar is said to have been deeply shocked by last weekend's scenes in which he was jostled and verbally abused by fans after the club's second defeat of the season. "He was ready to sell there and then," said a source close to Mr Sugar. "His commitment faltered, but he has gone away on holiday now to think on it."
ENIC already owns a big stake in Rangers, the Scottish football club, and is keen to expand into the English Premier League. Exploratory talks are understood to have taken place between Mr Sugar and ENIC's managing director, Daniel Levy, who is an acquaintance of Mr Sugar.
One possible stumbling block is UEFA rules which limits ownership to one competing European football club. ENIC, which has bought into a number of Continental clubs including AEK Athens and Vincenza Calcio, is already at loggerheads with the sport's ruling authorities over the issue.
However, one possible way round the rules would be for ENIC to acquire 29.9 per cent of Tottenham from Mr Sugar, just below the level that constitutes control, either with the balance of the stake placed in the market or taken up by ENIC's two powerful backers, SBC Warburg Dillon Reed, the investment bank, and Time Warner, the US entertainments group.
Any deal could also founder on price. Mr Sugar is reputedly asking a minimum of 80p a share for his stake, which would value the club at pounds 80m. But unless Tottenham's fortunes on the pitch improve dramatically, there would be few buyers at that price.
On present form, ENIC is not prepared to pay any more than the present stock market price of 63p a share.
Joe Lewis, a Bahamas-based billionaire, is planning to develop ENIC into an all embracing entertainments business taking in sports, theme restaurants and music.
Under the direction of Mr Levy and Mr Lewis's son, Charlie, ENIC has made a rapid expansion into football clubs and put in train ambitious plans for a chain of restaurants themed around the output of Warner Bros Studios.
Sources close to the situation put the chances of an imminent deal over Tottenham as remote. They also played down reports that Rupert Murdoch might be prepared to buy the stake.