CONCORD, New Hampshire – Republican Gov. Chris Sununu on Wednesday opened the door a bit to the possibility of taking on Democratic Sen. Jeanne Shaheen next year rather than running for re-election.

“I don't rule anything out,” the governor said when asked if he would rule out a GOP challenge against Shaheen, a former New Hampshire governor who’s running in 2020 for a third term representing the state in the Senate.

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If Sununu eventually decides to launch a Senate bid, it would give the GOP a high profile and popular candidate who could mount a competitive race against Shaheen, who’s also popular among Granite Staters.

Sununu’s comments generated a lot of buzz among some Republican Party officials in Washington, who would love to play offense in the 2020 cycle as they defend their 53-47 majority in the Senate. Twenty-two of the 34 seats up for grabs next year are held by the GOP.

Two of the top non-partisan political handicappers – the Cook Political Report and Inside Elections – currently rate Shaheen’s seat as "solid Democrat" and "likely Democrat."

A national GOP source told Fox News that party officials are looking toward Sununu as they try to pinpoint a candidate who could stay competitive with Shaheen.

Previously, the two-term New Hampshire governor had said he had “absolutely no interest” in running for the Senate.

But speaking with reporters Wednesday, the governor remarked that he’s not considering a run “right now.”

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Two recent public opinion surveys indicated a hypothetical matchup between Shaheen and Sununu would be tied.

Sununu highlighted that “one thing that was evident of those polls is people in the state want someone other than Jeanne Shaheen. Otherwise that poll wouldn’t have had her tied with someone who’s right now not even considering running.”

“I think the mandate is very clear. They want someone other than Jeanne Shaheen. Whether it’s myself or another candidate, she’s very vulnerable,” he emphasized.

If Sununu ended up facing off against Shaheen, it would be the third showdown between the two political families.

Then-Gov. Shaheen lost the 2002 Senate election to then-Rep. John E. Sununu, the current governor's older brother. Shaheen defeated the incumbent Republican senator in their 2008 rematch.

The New Hampshire Democratic Party highlighted Shaheen’s efforts on behalf of the Granite State and took aim at Sununu, who supports President Trump.

"Jeanne Shaheen is doing her job for New Hampshire - like fighting to protect funding at the Portsmouth Naval Shipyard from President Trump. Sununu ought to have the guts to join the Senator in standing up for New Hampshire rather than making phony political predictions,” longtime party chair Ray Buckley said.