British Apprentice star Lord Sugar has asked for the US President's help to be the next host of the American version of the show, after Arnold Schwarzenegger quit.
It comes after Schwarzenegger announced he would no longer be presenting the Celebrity Apprentice after just one series, amid poor ratings and a number of high-profile spats with the President.
The Terminator star blamed the show's "baggage" for his decision to leave and accused Mr Trump of driving away viewers with his continued involvement, which left a "bad taste".
But Mr Trump tweeted Schwarzenegger was not leaving voluntarily and had been "fired by his bad (pathetic) ratings, not by me".
However, Schwarzenegger fired back saying: "You should think about hiring a new joke writer and a fact checker."
In his message to the Republican tycoon, Lord Sugar alluded to a feud between himself and the President.
He wrote: "Mr President can we bury the hatchet, please ask NBC to let me do the next series of the Apprentice. You know I can do it."
Last September, the peer hit back at claims by Mr Trump that when he was first chosen to host the UK version "he didn't fit the role".
Mr Trump told Good Morning Britain: "He works for me. He is a small timer. I mean, he's doing a nice job but don't forget, he works for me I make money from The Apprentice.
"When we first chose him for the show, he was so low on the economic scale, he didn't really fit the role.
"I think he's made more money by being on The Apprentice than he has in business."
Lord Sugar responded at the time saying: "It's complete and utter nonsense, and he's got nothing to do with this programme, other than that he was once the host of the American show."