Trump will also sit down Tuesday with Senate Foreign Relations Committee Chairman Bob Corker, R-Tennessee, and House Homeland Security Committee Chairman Michael McCaul, R-Texas.
The meetings, confirmed by Republican National Committee chief strategist Sean Spicer, come as Trump fills key foreign policy posts in his incoming administration.
The Romney meeting, in particular, takes place amid speculation that Trump could tap the 2012 GOP nominee, who’d trashed him during the 2016 race, for secretary of state — an idea Trump campaign manager Kellyanne Conway has criticized in recent days on Twitter and in TV appearances.
“I’m all for party unity, but I’m not sure we have to pay for that with the secretary of state position,” Conway told CNN’s Dana Bash on “State of the Union.”
She added: “It’s just breathtaking in scope and intensity the type of messages I’ve received from all over the country … the number of people who feel betrayed to think that Gov. Romney would get the most prominent Cabinet post after he went so far out of his way to hurt Donald Trump.”
Trump’s meeting with Petraeus could lead to the appointment of a high-profile veteran of the US’s foreign conflicts in recent decades.
But Petraeus, like Trump’s national security adviser pick, retired Lt. Gen. Michael Flynn, has a history of mishandling classified information — what Trump had accused his general election opponent, Hillary Clinton, of doing via her private email server.
Petraeus, a former CIA director who oversaw military operations in Afghanistan and Iraq, previously faced charges of removing and retaining classified information as part of his romance with biographer and lover Paula Broadwell. He was sentenced to serve two years of probation and pay a $100,000 fine.
Petraeus had said last week he would serve in Trump’s administration if asked.
The four-star general told BBC Radio 4’s flagship “Today” program that if Trump asked for his help, “the only response can be: ‘Yes, Mr. President.'”
Trump asked Corker to meet with him. The two spoke after Trump’s victory, but have not had a face-to-face meeting since the summer, when Corker was under consideration for the vice presidential nomination that ultimately went to Mike Pence. Their staffs have spoken since election night, though, a source told CNN.
CNN’s Ashley Killough and Manu Raju contributed to this report.