His remarks came shortly after Angela Rayner resigned as Deputy Prime Minister on Friday, 5 September.
Farage claimed there is a "big rift" within the Labour party.
He suggested some Labour MPs might believe they have a better chance of re-election under a "Jeremy Corbyn sectarian ticket" than under Sir Keir Starmer.
Rayner resigned after an ethics adviser found she breached the ministerial code by underpaying stamp duty on her £800,000 flat in Hove, East Sussex.