The pair head up separate versions of the reality series The Apprentice in the US and UK. After Sir Alan accused the US billionaire of being loud, garish and "full of himself", Mr Trump hit back yesterday to claim that his UK rival owes him all his TV success. And he said that he was making more out of the rights to the BBC version of the hit series than the fee Sir Alan was earning from the show.
"I make more money from his show than he does," said Mr Trump. "Generally when someone does the Trump role it doesn't work out as successfully, and in Alan's case that's also true. I mean it's OK, but I've heard it's not exactly the American version, is it?"
In The Apprentice, Sir Alan and Mr Trump lead the hunt for a wannabe understudy to join their respective business empires. Each week a candidate is eliminated after being torn to pieces for their shortcomings and told, with a jab of the finger: "You're fired!"
The gloves came off after Sir Alan, the outspoken boss of electronics firm Amstrad, launched a withering attack on Mr Trump's flamboyant style in his version of the show. "I'm not like Trump, showing off his apartment," he said. "He's so full of himself. There are different types of business ego. Some people just want to show you all the stuff they've got. I just like to show off about how clever I am in business."
The hard-nosed ex-Tottenham Hotspur chairman accused Mr Trump of being "loud and garish" about his achievements - unlike British business gurus.
But Mr Trump, 59, who is said to have amassed a fortune of £1.5bn, hit back with a forthright attack on his rival. "He's only there because of me, so I consider that he works for me - and I don't say anything bad about my employees. I wish his show was as big a success in Britain as my show is in America, but I'm very happy that the British version pays me lots of money," he said in an interview with the Daily Mail yesterday.
The Apprentice began broadcasting in the US in 2004, with Mr Trump as the executive producer. The UK version launched a year later. The second series of Sir Alan's show, currently midway through its run, has been pulling in more than four million viewers a week.
More than 10,000 people applied to take part, competing for a six-figure salary within the Amstrad organisation.
Sir Alan, also 59, may need to watch his back if Mr Trump is feeling particularly put out by the comments, as the American tycoon is heading to the UK next week. He will be visiting his planned £300m golf tourism development on the Menie Estate near Balmedie in Aber-deenshire, where he has vowed to build the finest golf resort in the world.