If asked to join Trump's administration, Petraeus told BBC Radio 4 in an interview last week, "The only response can be 'Yes, Mr. President.'"
Romney and Petraeus are contenders for secretary of state, according to senior level sources.
The decision of whom to pick as secretary of state has created a divide among Trump’s advisers. These competing views came to light in ABC News interviews and conversations with multiple officials in the Trump transition, who have spoken on condition of anonymity.
Advocates for former GOP presidential nominee Romney, who has international renown from his time running the 2002 Salt Lake City Olympic Games, say his selection would send a signal of reassurance to the country and show flexibility in Trump's choices for his administration.
Last week Trump's campaign manager, Kellyanne Conway, tweeted that she was "receiving [a] deluge of social media & private comms" and linked to a Politico story about Trump loyalists warning against Romney as secretary of state.
Then over the weekend she mentioned the two politicians' very contentious relationship during the campaign and said Romney went "out of his way" to damage Trump.
"I think that there was the never-Trump movement and then there was Gov. Romney," Conway said Sunday in an interview with "This Week." "He went out of his way to hurt Donald Trump. He gave two speeches that I can recall in this calendar year, and they were both about Donald Trump."
Romney withheld his endorsement throughout the election cycle. He also delivered an impassioned and personal speech in March against Trump as the party's nominee, calling Trump a "phony, a fraud." During the Republican primaries, when the remaining candidates were Trump, Texas Sen. Ted Cruz and Ohio Gov. John Kasich, Romney recorded robocalls for Cruz, arguing, "A vote for John Kasich is a vote for Donald Trump."
referring to independent candidate Evan McMullin, Conway said on Sunday, "As McMullin ran in the state of Utah for president, we don't know who Mitt Romney voted for."
But she also said she's "very pleased" that Trump and Romney met earlier this month, in Bedminster, New Jersey.
"I only wish Gov. Romney had been as critical of Hillary Clinton and her policy positions," Conway said on "This Week," adding, "So we're all for party unity. I don't think a cost of admission for party unity has to be the secretary of state position."
She wouldn't elaborate on why she aired her concerns about Romney on Twitter or if Trump asked her to send that tweet. "I won't discuss that. But I will tell you that I've already weighed in privately because I've been asked to," she said.
ABC News' Luis Martinez contributed to this report.