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.
“It was a warm and a substantive exchange and I know he is under active consideration to be secretary of state (…) along with some other distinguished Americans,” Mr Pence told the Fox News Sunday programme.
In March, during the Republican primary race, Mr Romney said Mr Trump had neither “the temperament nor the judgement to be president”, accusing him of bullying, misogyny and dishonesty.
“Prospects for a safe and prosperous future are greatly diminished” if Mr Trump became the nominee, he said.
Media captionDonald Trump said his meeting with Mitt Romney ‘went great’
Mr Trump responded by mocking Mr Romney, calling him a “failed candidate” and a “choke artist”.
However, US media have suggested that the role of secretary of state could be up for grabs. In the past, Mr Romney has taken a far more critical line on Russia than that suggested by Mr Trump.
Mr Trump has settled several posts so far, a number of them controversial.
The nominee for attorney general, Jeff Sessions, who was rejected from becoming a federal judge in 1986 because of alleged racist remarks
Lt Gen Michael Flynn, who is to be national security adviser and has drawn concern over his strident views on Islam
Mike Pompeo, a combative congressman who is a fierce critic of former Secretary of State Hillary Clinton
Chief strategist Stephen Bannon, the driving force behind the right-wing Breitbart News website.
Media captionThe cast of the Broadway hit musical Hamilton address Mr Pence
The sounds of freedom?
Mr Pence was asked about the way he was treated when attending a performance of the Broadway musical Hamilton on Friday.
The audience booed the vice-president elect and a cast member read out a letter saying “diverse America” was “alarmed and anxious” at the future administration.
Mr Pence told Fox News Sunday that he was relaxed about it and had said to his daughter during the incident: “That’s what freedom sounds like.”
But Mr Trump renewed his criticism of the cast on Sunday.
“The cast and producers of Hamilton, which I hear is highly overrated, should immediately apologize to Mike Pence for their terrible behavior,” he tweeted.
On Saturday Mr Trump tweeted: “Our wonderful future V.P. Mike Pence was harassed last night at the theater by the cast of Hamilton, cameras blazing. This should not happen!”
Hamilton won the 2016 Pulitzer Prize for Drama, along with 11 Tony awards for live theatre. Tickets to the show are the most coveted on Broadway, sometimes changing hands for thousands of dollars.