Story highlights Romney and Trump met this past weekend at Bedminster, New Jersey

A Romney appointment would give Trump instant gravitas abroad

Washington (CNN) Mitt Romney is taking a potential offer to serve as Donald Trump's secretary of state seriously, even as questions remain about whether Trump considers a Romney nomination as plausible.

A source familiar with transition discussions said Romney is seriously considering the posting, which has not yet been offered. Romney is certainly discussing the prospect with his family members who often serve as his closest advisers, the source said, though a decision is not likely until after the Thanksgiving holiday.

Two transition sources say Romney is one of the leading contenders for the job but others remain in the mix, including former New York City Mayor Rudy Giuliani, according to one of the sources.

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Romney and Trump met this past weekend at Trump's golf retreat in Bedminster, New Jersey , where the two men discussed world affairs and the possible position. Vice President-elect Mike Pence has since confirmed that Romney is under "active consideration" for the job as America's chief diplomat.

A Romney appointment would give Trump instant gravitas abroad and a marquee name in one of the highest-profile administration postings. The Trump campaign has praised Romney in recent days, even as it stresses that other officials are under consideration for the secretary of state position.

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