Republicans close to Mr. Romney believe Mr. Portman is on the list, along with a handful of others including former Gov. Tim Pawlenty of Minnesota, Representative Paul D. Ryan of Wisconsin and Gov. Bobby Jindal of Louisiana. The roster could be larger, associates of Mr. Romney caution, but many Republicans argue that Mr. Portman is ideally suited for campaigning in Ohio and other critical Midwestern states.“He would probably be the best-prepared person of anyone since George Herbert Walker Bush became Ronald Reagan’s vice president,” said Joe Hagin, who also worked in both Bush administrations and has known Mr. Portman since childhood. “He has an immense understanding of the budget, the tax code and trade and foreign policy.”Mr. Portman, 56, has close ties to the Bush family. Barbara Bush recorded radio advertisements that helped him win an early Ohio Congressional race. This week in Maine, Mr. Portman is scheduled to have lunch with the elder George Bush, whom he served in the White House as associate counsel and head of legislative affairs.Friends of both men say they are not certain if Mr. Bush has shared his admiration for Mr. Portman with Mr. Romney — any such talk would be private, presumptuous or both, one associate said. But the former president praised Mr. Portman when asked about him last week.