Exxon Mobil Corp Chief Executive Officer Rex Tillerson emerged on Friday as President-elect Donald Trump’s leading candidate for U.S. secretary of state, a senior transition official said.

Trump met Tillerson on Tuesday and may talk to him again over the weekend, the official said. Trump appears to be in the final days of deliberations over his top diplomat with an announcement possible next week.

Tillerson’s favored status was revealed as former New York Mayor Rudy Giuliani formally withdrew from consideration for secretary of state.

The transition official, who spoke on condition of anonymity, said Tillerson, 64, had moved ahead in Trump’s deliberations over 2012 Republican presidential nominee Mitt Romney, who has met Trump twice, including at a dinner in New York.