Conservative MPs are due to choose the two men who will contest the final stage of their leadership race later.
The remaining field of four candidates will be whittled down to three in another secret ballot, with the result expected at about 13.00 BST.
There will then be a further vote to select the final two, one of whom will be elected leader by party members.
Boris Johnson topped Wednesday's third ballot with 143 votes, ahead of Jeremy Hunt, Michael Gove and Sajid Javid.
International Development Secretary Rory Stewart was knocked out of the contest on Wednesday evening, after he secured the backing of just 27 Tory MPs.
Mr Johnson is almost certain to make the run-off of 160,000 or so Conservative members who will elect the next Tory leader - and prime minister - in a postal ballot, starting next week