Sen. Rob PortmanRobert (Rob) Jones PortmanSenate moving ahead with border bill, despite Trump 13 GOP senators ask administration to pause separation of immigrant families Lawmakers, businesses await guidance on tax law MORE (R-Ohio) on Tuesday did not rule out a run for the GOP presidential nomination in 2016. 

Portman, in an interview published Tuesday, said he is not particularly eager to run but signaled that a weak GOP field could change his mind. 

“I’m not particularly eager to do it myself, and having been involved in six presidential campaigns, I know what it’s like,” Portman told The Washington Post. “But if nobody running is able to win and willing to address these issues, then I might have a change of heart.”

Portman was elected to the Senate in 2010 and is up for reelection in 2016. He said that is the only office he is running for at the moment. Like other potential candidates, he said he would wait until later this year or early next year to make a decision. 

“Let’s see what happens, let’s see who runs. For the moment, I’m up for reelection in Ohio, so that’s my plan," he said.

Ohio law allows candidates to run for both offices at the same time, Portman said, but he disagrees with it. 

"I'm told the Buckeye state rule is your are allowed to do both, and I don't think it is a good idea," He said in a later interview on the Hugh Hewitt radio show. 

Portman was the first GOP senator to come out in favor of gay marriage last year, after finding out his son was gay. He said the conversion has opened the door to other constituencies to talk about economic issues. 

“To win a national election, we’ve got to work on fixing the Republican brand, and that’s what I’ve been working on,” Portman said. “We’ve got to be the party of ideas, not the party of no."

Portman hails from a battleground state that has becoming increasingly important in presidential elections. Cleveland was named Tuesday as the site of the Republican National Convention in 2016

The 2012 Republican nominee, Mitt RomneyWillard (Mitt) Mitt RomneyFormer top Treasury official to head private equity group Romney backs Laura Bush on border: 'We need a more compassionate answer' ‘Three Californias’ plan would give Dems more seats MORE, told the Post that Portman would be a credible candidate if he were to step up — a comment he has made about a number of other candidates. 

Romney said the nominee would likely be a mainstream, practical Republican, similar to Portman.  

“Rob has demonstrated a kind of practicality that is appealing,” Romney said. “There is a stream in my party that is anxious to fight but not as concerned with winning, and I think that’s the minority stream."

Portman was considered a potential vice presidential nominee to Romney in 2012 before Rep. Paul Ryan (R-Wis.) was picked. The Ohio senator helped out on the campaign, subbing in for President Obama during debate prep. 

Portman is a former House member and George W. Bush administration official. He was nominated as the U.S. Trade Representative, then the director of the Office of Management and Budget during Bush's second term.

If he does decide to run, he will likely have company from the Senate. GOP Sens. Rand Paul (Ky.), Marco Rubio (Fla.) and Ted Cruz (Texas) are also considered potential candidates. 

— Updated 6:40 p.m.