WASHINGTON — President-elect Donald Trump moved closer to nominating Exxon Mobil CEO Rex Tillerson as his secretary of state Saturday, meeting privately with the business leader for the second time in a week. Trump’s transition team cautioned that no announcement was expected over the weekend. Trump has privately signaled that he plans to tap Tillerson for the powerful Cabinet post, but had not formally offered him the job as of Saturday afternoon, according to people who have spoken with Trump and his transition team. Some advisers worry that Tillerson’s ties to Russia would lead to a contentious Senate confirmation hearing and keep alive questions about Trump’s own relationship with Moscow. The CIA has assessed with “high confidence” that Russia sought to influence the U.S. election on behalf of Trump, who spoke throughout the campaign about improving Washington’s relationship with Moscow. Tillerson rose to prominence through Exxon’s Russian energy business and was awarded Russia’s Order of Friendship. The president-elect’s deliberations over his pick to lead the State Department — particularly his consideration of Mitt Romney for the post — have exposed anew the deep rivalries within Trump’s team. Campaign manager Kellyanne Conway warned publicly that Trump supporters would feel betrayed if he were to choose a fierce rival for the post, especially given that some loyal allies — most notably former New York City Mayor Rudy Giuliani — also wanted the job. Giuliani officially took himself out of consideration for the Cabinet on Friday, though his standing had already been diminished. In addition to Romney, Trump has also been considering Tennessee Sen. Bob Corker and John Bolton, the former U.S. ambassador to the United Nations.