Portman, who served six terms in the U.S. House of Representatives, is just one of the possible choices for McCain, The Columbus (Ohio) Dispatch reported Sunday.
Political observers say Portman could play a pivotal role for McCain.
Portman, an attorney in Cincinnati, served in the Bush administration as U.S. trade representative and then as director of the Office of Management and Budget. At age 52, Portman would add relative youth to the GOP ticket with McCain, 71.
"You don't pick him because you want to win Ohio, you pick him because he brings to the table a breadth of experience few others can match," said Neil Newhouse, a GOP pollster.
Portman said he has spoken several times with McCain recently, but the topic of the vice presidency hasn't been mentioned.
"I appreciate some people have put me on their ... list, but there are a lot of other great choices," Portman told the newspaper.