The 2012 Republican presidential nominee and one of Trump's most vocal Republican Party critics during this year's election campaign, met privately with the President-elect for about an hour at Trump's private golf course in Bedminster, New Jersey.
After the meeting, Romney offered no hint as to whether he was offered or would accept a role in Trump's administration.
"We discussed those areas, and exchanged our views on those topics - a very thorough and in-depth discussion in the time we had," Romney, 69, said.
"I appreciate the chance to speak with the President- elect and I look forward to the coming administration and the things that it's going to be doing," said Romney, who during the Republican primary had described Trump as a "con man" and had asked his supporters not to vote for Trump.
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Trump walked Romney out at the end of the meeting and said "it went great." He did not take any questions.
It is being speculated that Trump is considering Romney for the position of Secretary of State in his administration.
For Trump, Romney, a former Governor of Massachusetts would bring an immediate burst of knowledge, global credibility, sound temperament and competence to his nascent administration, CNN reported.
His selection would also be seen as a genuine gesture to bind the wounds in the Republican Party and the foreign policy establishment left over from a bitter primary campaign.
And since Trump's core voters are more concerned with draining the swamp of well known Washington insiders than foreign policy, the State Department may be one place he could put an establishment figure and not sustain much political damage, it said.
"Mr Romney would be a great choice in a sense that would be a signal sent to moderates as well as conservatives," William Cohen, a former US defense secretary, said.
That is because Romney is squarely within the parameters of accepted US foreign policy orthodoxy, is an internationalist, is well known abroad, and is committed to the notion of free trade, US alliances and a robust US posture in the world, CNN reported.