"I just got elected two years ago," Portman, R-Ohio, told a Denver fundraising event Wednesday night, one of five he attended in the battle ground state that day.
"I think that's where I'm going to end up staying," he said when asked his thoughts about possibly leaving the Senate to join the presumptive Republican presidential nominee's ticket.
"I think it's a very important position right now," he said of his Senate role, pointing to pressing issues such as government debt, the deficit, energy resources and healthcare issues.
"And right now Congress is paralyzed. And we're really in kind of a partisan gridlock," he said. "We need leadership, and that's where I intend to stay. I think I can really help in there.
"That's where I think I'll end up being."
It was unclear if Portman was simply keeping the guessing game going or providing clues to his plans.
The Romney campaign had no immediate comment.
The former Massachusetts governor and his campaign have offered no apparent clues about the vice presidential selection.
Romney advisers have tried to use the mystery to add momentum and to raise money, analysts say.
"Even I haven't been able to get so much as a hint out of him," Romney son Craig Romney said in a fundraising e-mail to supporters this week.
The Financial Times reported Romney could announce his selection as early as Thursday, ahead of a four-day bus trip across battleground states.
The Republican National Convention, where GOP delegates will choose the party's nominees for president and vice president, will be in Tampa, Fla., the week of Aug. 27. Presidential candidates almost always announce their running mates before the national convention.
Beyond Portman, other names political watchers point to include House Budget Committee Chairman Paul Ryan, R-Wis., widely seen as one of the party's most influential voices on economic policy, and former Minnesota Gov. Tim Pawlenty, who ran his own campaign for president until a year ago but has been a big Romney booster since dropping out.
Politico says Ryan advocates, including high-profile conservative elites, believe Romney, 65, will lose if he doesn't launch a political offensive against President Barack Obama, 51.
They say selecting Ryan, 42, would sound a clarion call to the electorate about the sort of reforms Romney wants to bring to Washington, Politico says.
Pawlenty commented on his vice presidential prospects to Romney supporters in Jackson, Mich., Wednesday, saying, "We'll know soon enough."
Notable deaths of 2014 [PHOTOS]