The two have been at loggerheads over UKIP's future direction and strategy.
Ex-UKIP leader Nigel Farage has called for the party's only MP to be sacked over claims he is trying to divide the "kippers" in every "imaginable" way.
Embattled leader Paul Nuttall broke off from his holiday to ask party chairman Paul Oakden to haul in Mr Carswell for a meeting about the row.
Aaron Banks threatened to pull his funding unless he is made chairman so he can "purge" members and stop it being "run like a jumble sale".
Mr Farage stepped up his attacks on Mr Carswell as the row intensified over claims that he played a role in blocking a knighthood for the former leader.
Still "very close" to his former Tory colleague MEP Daniel Hannan, Mr Carswell is said to have greatly opposed immigration during the referendum campaign because his "middle-class friends" would have been "put off" from voting Leave.
Mr Banks has described Mr Carswell, whose relationship with Mr Farage is also strained, as a "terrible individual who has done his best to destroy UKIP".
Mr Banks added: 'The vast majority of Ukip people are lovely people but there is an element that causes trouble and if I was in charge I would want to eliminate all of that'. "UKIP MP or not, I'll stand against him in Clacton next election!"
Mr Farage has claimed the party's only MP has been "totally disconnected" from UKIP since February 2015 and it was time for him to sever his links entirely.
Writing in The Telegraph, Mr Farage said: 'As a party, how can we let a man represent us in the House of Commons who actively and transparently seeks to damage us? I'm trying to double the size of the Ukip parliamentary party at the moment. The time for him to go is now'.
UKIP's only MP has discussed re-defecting back the Conservatives at the next election with senior Tories, the Sun can reveal.
Mr Carswell, who has urged the party to project a more positive image and tone down its rhetoric on immigration, has warmer relations with Mr Nuttall and several of his key advisers.
Ukip is in an increasing state of turmoil after failing to win the Stoke Central by-election last Thursday.
Mr Banks criticised Mr Nuttall's tactics in the Stoke campaign, saying he wrongly adopted a "red UKIP" strategy, copying Labour policies on the NHS.
'Mr Carswell is a career politician and doesn't care about Ukip and he has got to get out, ' the businessman said.