The Home Secretary secured 34 votes in the fourth leadership ballot, trailing behind Mr Gove on 61 and Mr Hunt on 59.
The result of the fifth and final ballot will be announced this evening, confirming the final head-to-head contest between one of the two cabinet ministers and Boris Johnson.
He said he was "delighted to have the support of over half of all Conservative MPs in the fourth ballot". Boris Johnson supporter Mark Francois said: "He is almost certainly in the final. And the question is who is his opponent going to be? And its very close."
The former foreign secretary gained 14 votes compared with the third ballot, when Rory Stewart was eliminated, while Mr Javid lost four votes.
The figures will add to speculation that the votes of Mr Johnson's supporters were 'loaned' to Mr Javid on Wednesday to ensure Mr Stewart was eliminated.
Mr Gove secured 61 votes, up 10 from the previous vote, while Mr Hunt was on 59, up five. There were two spoiled ballots.
Mr Hunt had been second in each of the three previous rounds of voting.
A Johnson-Gove contest would be the culmination of their infamous falling out in the 2016 leadership race, when the two main derailed each other's campaigns after having delivered Brexit together.
A source in Mr Gove's campaign said: "This is a great result. We are in a strong position to make the final two where we can have a civilised debate in the country."
The Environment Secretary's backers signaled that they would target Mr Hunt over his vote to remain in the EU in 2016, with one telling The Scotsman that unless the final two candidates are both Brexiteers, "I'm afraid the result will be very predictable."