The statement, in a Fox News interview, comes after President-elect Donald Trump met Mr Romney, a Republican who criticised him during the campaign.
There has been speculation that the post of top diplomat was discussed.
Neither man gave details of their meeting on Saturday. Mr Romney said talks had been "far-reaching".
Mr Romney, who ran an unsuccessful campaign against Barack Obama in 2012, met Mr Trump at the president-elect's golf course in Bedminster, New Jersey.
