The Romney campaign also circulated a memo to reporters Monday morning penned by Portman and Sen. Pat Toomey (R-Pa.) ahead of President Obama's bus tour through the two states.
"This week, President Obama will visit our states as he campaigns for reelection," the senators wrote. "We welcome him, and we hope he takes time to learn about how the private sector is actually doing and about the challenges facing our constituents in Ohio and Pennsylvania."
Portman has thus far downplayed speculation in his public comments.
"I'm probably best suited where I am," he told the Cleveland ABC News affiliate last week, adding that if Romney asked, he would "say there are a lot of other great choices."