The former Army officer voiced his opinions on the ITV’s Peston on Sunday amid mounting calls for his resignation.
Mr Bolton faced backlash when texts from his former partner were revealed which made highly offensive comments about Meghan Markle and black people.
Ukip's national executive committee (NEC) is said to be planning to hold a vote of confidence in their leader during a special meeting on Sunday.
Mr Bolton told Mr Peston the party could not afford to have another leadership contest.
He added: "If the NEC decides to go down the road of months of further in-fighting and further negative media scrutiny by deciding to pass a vote of no confidence in me, I think that the reality is that the party is probably over."
Mr Bolton said previously his "romantic" relationship with 25-year-old model Jo Marney was over following an outcry sparked about a series of shocking comments she made.
But he admitted they were "still in touch" after pictures emerged of them meeting up.
Asked if he was going to quit, the party leader replied: "No I'm not, no."
"A leadership contest now would be financially almost un-viable for the party," he added.
Mr Bolton left wife Tatiana, 42, who gave birth to their second daughter at London's St Pancras station in 2016 after going into labour on a train, prior to his relationship with Ms Marney becoming public in early January.
He told the programme: "I don't believe I have done anything wrong.
"My own personal life, it's a little bit of a mess at the moment. I need to sort that out, of course."
Asked about reports his estranged wife still did not know if their marriage was over, he replied: "My wife and I have exchanged lengthy emails on this. We have spoken a couple of times on the phone, but that is my business."
Ukip chairman Paul Oakden is said to have emailed party members on Saturday, saying the NEC does not have powers to remove Mr Bolton and a new leader can only be chosen through a ballot of members.
In the message shared by activists online, Mr Oakden called for unity, adding: "Let's all come together to sort this out and put this party back on the road."