Bob Asher, the state's Republican national committeeman, said he met with Ridge in recent days and urged him to run.
"Governor Ridge is very serious about considering to run, and he is weighing his options," Asher said.
Ridge and Specter, who stunned political observers last week by switching his party affiliation from Republican to Democrat, are two of Pennsylvania's best-known politicians. An election showdown between them is certain to garner national attention and generate large campaign contributions from outside the state.
A Quinnipiac University poll released Monday showed Specter and Ridge running about even in a hypothetical general-election race. The survey showed Ridge, who has not run in an election since 1998, with a 55 percent favorability rating and Specter with a 52 percent rating.
Ridge, 63, served 12 years in Congress before he was elected governor in 1994. He stepped down during his second term after President George W. Bush tapped him to head what would become the Department of Homeland Security after the Sept. 11, 2001, terrorist attacks. He left that post in 2005 and now runs a Washington-based consulting firm, Ridge Global LLC.
In last year's presidential campaign, Ridge was mentioned as a possible running mate for the Republican nominee, Sen. John McCain, of Arizona. Ridge is a combat veteran of the Vietnam War, like McCain, and was awarded the Bronze Star for bravery.
Specter, 79, is seeking a sixth Senate term. He said he decided to end his four-decade relationship with the Republican Party because he was unlikely to win the nomination in a party that has grown increasingly conservative.
He announced his switch less than two weeks after former U.S. Rep. Pat Toomey, who came within 2 percentage points of beating him in the 2004 primary, announced that he planned to challenge the incumbent again in 2010.
Specter's campaign declined to comment on Ridge's prospective candidacy.
Toomey, who for the past four years headed the Washington, D.C.-based Club for Growth, a politically active conservative group that promotes a smaller government and lower taxes, issued a statement through his campaign that sought to paint both Ridge and Specter as too liberal for the GOP.
It said Toomey "is the candidate with the consistent record of standing up for taxpayers that is needed to win the GOP primary, who has a track record of winning general elections in Democratic-leaning areas."
But Rob Gleason, the state Republican chairman, said Ridge would be "a great candidate."
"It would be exciting to have him" on the 2010 ticket, Gleason said. "He would definitely beat Specter - hands down."
Specter faces opposition in the Democratic primary from Philadelphia-area civic leader Joe Torsella. U.S. Rep. Joe Sestak also has said he may enter the race.
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Associated Press writer Mary Clare Jalonick in Washington contributed to this report.
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