Boris Johnson and Rishi Sunak, contenders to be the next U.K. prime minister, held face-to-face talks Saturday to discuss the Conservative leadership contest, according to people familiar with the discussions, seeking a deal that would eliminate the need to take a potentially divisive runoff vote between them to party members.

The former prime minister and ex-chancellor spoke as some Tory MPs called on them to put aside their differences and thrash out a deal that would see one of them take over as prime minister and the other serve in a senior Cabinet position, the people said, declining to be identified because the matter is private.

The prospect of the pair running on a joint ticket represents yet another unimaginable twist in what’s been a chaotic year in U.K. politics. The chances of a deal were previously considered almost impossible due to the fallout between the two men, the people said. They became bitter enemies this summer when Sunak resigned as finance minister of Johnson’s administration, a move that helped trigger his downfall.