The two often make news media and blogger lists of potential 2008 running mates for their parties. Ohio, which narrowly put President Bush over the top in 2004, again figures to be crucial with 20 electoral votes at stake, adding to speculation that the state nicknamed "the Mother of Presidents" could birth a vice presidential candidate this time.
"In the context of a national campaign in which Ohio is a key state, both those names make a lot of sense," said Herb Asher, an Ohio State University political analyst. "They're not exactly national household names, but if the question is, is there a running mate that could help deliver a key state, both could be able to do that."
Portman, overwhelmingly re-elected six times to Congress in southern Ohio, has been projected as a possible challenger to Strickland's 2010 re-election since returning to Ohio last year after leaving his job as President Bush's budget chief. He endorsed Arizona Sen.on Tuesday, drawing more mentions as a possible running mate.
"I like being home with my family," Portman, who also served as U.S. trade representative, said in an interview. "I'm not looking to go back to Washington right now."
Portman, also considered a potential Senate candidate, said he doesn't see himself on this year's ticket and that there are plenty of other strong VP candidates. He said he does plan to campaign hard to help McCain win Ohio, a state no Republican has won the presidency without.
Strickland, meanwhile, was an early supporter of Sen.'s campaign and the statewide vote-getting ability of the former congressman's 2006 landslide lands him on Democratic lists.
"That talk comes from the importance of Ohio in a general election," Strickland said in an interview. "It says more about the importance of Ohio than it does about Ted Strickland as an individual."
Strickland said he's committed to leading Ohio as governor and would politely but firmly decline if an offer did come. "But I will try to do my part to get a Democrat elected from Ohio," he said.
Merle Black, a political scientist at Emory University in Atlanta, said Portman, 52, has little national name recognition. Black agrees that McCain needs a younger conservative to offset concerns about his age - 71 - and about his appeal to the party's staunch right-wingers, but he thinks someone with a governor's statewide experience is more likely.
Former Arkansas Gov., still chasing McCain for the nomination, is generally considered a possible running mate. Other Southerners mentioned include Govs. Charlie Crist of Florida, Mississippi's Haley Barbour and South Carolina's Mark Sanford.
But Black said if McCain has to worry a lot about winning in the South, he probably would lose the election anyway. Black thinks someone from the Midwest could have appeal.
Gov. Tim Pawlenty of Minnesota is among Midwesterners whose names are bandied about for McCain's ticket. If not for the age issue, Sen. George Voinovich, former Ohio governor but also age 71, would likely be high on GOP candidate lists.
On the Democratic side, those getting mentions include former Iowa Gov. Tom Vilsack, who's been campaigning in Ohio for Clinton, and one with Ohio roots - Gov. Kathleen Sebelius of Kansas, a Cincinnati native and daughter of former Gov. John Gilligan. Sebelius, who endorsed Sen.before he won her state's party caucuses Feb. 5, said after a recent rally here that she's focused on her current job and just trying to help Obama where she can.
"I think it's way too early," she said of running mate talk.
Ohio seems overdue after sending eight men to the presidency, a run that ended with the 1923 death in office of Warren Harding.
"We used to say 'the Mother of Presidents' is on the pill now," said a chuckling Gilligan, himself part of national speculation until his 1974 re-election loss. "I don't know what happened. We've had some pretty outstanding political leaders in this state, but they've never risen to the right level."