Senate Minority Leader Mitch McConnell (Ky.) could have a strong hand in the operations of the Republican National Committee in the 2010 election cycle should RNC Chairman Mike Duncan win another term at the helm.

Duncan, a Kentucky native and friend of McConnell’s going back 40 years, has yet to decide if he’ll run for another term as RNC chairman. Asked if his relationship with McConnell might prove useful should he seek another term, Duncan demurred. But he didn’t dismiss the idea, either.

“I don’t have any view on whether that gets or loses me votes on the committee,” Duncan said Wednesday during a brief telephone interview while in Florida to attend a meeting of Republican governors.

Duncan said his priority now is his day job as RNC chairman, which means doing everything he can to ensure that McConnell is the leader of a Republican minority in the 111th Congress that can muster a filibuster. McConnell is staged to win another two-year term as the top Senate Republican, arguably his party’s most powerful post with a Democrat set to take over the White House.

If Duncan seeks the RNC job again, he is looking at a potentially crowded field of competitors. Among the possible candidates are former Speaker Newt Gingrich (Ga.), outgoing Sen. John Sununu (N.H.), former Maryland Lt. Gov. Michael Steele and outgoing Office of Management and Budget Director Jim Nussle.

In the meantime, Duncan said he is focused on helping Sen. Saxby Chambliss (Ga.) win his Dec. 2 runoff against former state Rep. Jim Martin (D), and aiding Sen. Norm Coleman (Minn.) in his recount endeavor. The RNC is currently on the ground and active in both states.

Coleman won re-election over comedian Al Franken (D) by just 201 votes, a narrow enough margin to trigger an automatic recount according to Minnesota law.

Chambliss finished ahead of Martin on Nov. 4, but failed to secure the 50 percent of the vote needed under Georgia law to avoid a runoff. Should Chambliss and Coleman prevail, the Senate Republican Conference would number 42, leaving the Democratic majority two votes shy of being filibuster-proof.

Duncan said he hasn’t talked to McConnell about any future he might — or might not — have at the RNC. But he said the two have talked about the Georgia and Minnesota Senate races.

Duncan did not mention Alaska, where Sen. Ted Stevens (R) is leading Anchorage Mayor Mark Begich (D) by a few thousand votes with tens of thousands left to count. Most Republicans, including McConnell, have called for Stevens to resign in the wake of his conviction last month on seven felony counts for filing false financial disclosure statements.

Should the Republicans manage to hold onto the Alaska Senate seat, their Senate minority would reach 43.

Meanwhile, Duncan also labeled as one of his priorities winning Louisiana’s open 4th district.

The contest to succeed Rep. Jim McCrery (R) — scheduled for Dec. 6 — was pushed back following a hurricane that forced the state to delay its primaries and any subsequent runoff elections.