Sen. Richard Burr (N.C.), one of the Senate Republicans’ most ambitious junior members, will not run for a leadership position in the 111th Congress, a source close to Burr says.

“Leadership is not something he was shooting for. He was first approached last time by some of his colleagues. That’s what got him in that race,” said the source, referring to Burr’s unsuccessful run last year for Conference chairman against Sen. Lamar Alexander (Tenn.).

Burr had been mentioned as a possible candidate for vice chairman of the GOP Conference, along with Sens. Lisa Murkowski (Alaska) and John Thune (S.D.). So far, Thune is the only Senator to publicly announce a bid for the slot.

Meanwhile, Sen. John Cornyn Texas), the current vice chairman of the Republican Conference, is running for chairman of the National Republican Senatorial Committee. Sen. Norm Coleman (Minn.) also is interested in that post, but is awaiting a post-election recount to see if he has secured a second Senate term.

The current NRSC Chairman John Ensign (Nev.) is running unopposed for the Republican Policy Committee job now held by Sen. Kay Bailey Hutchison (Texas). Hutchison isn’t seeking another two-year term in that position in order to pursue a gubernatorial bid.