Nebraska Sen. Mike Johanns will not seek the Republican Conference Vice Chairman position that will be open in the wake of Sen. Lisa Murkowksi’s loss last month in the Alaska Senate primary.

Johanns and Wyoming Sen. John Barrasso were deemed by GOP sources the most likely candidates to seek the leadership post held by Murkowski. But Johanns told the Lincoln Journal Star newspaper Tuesday that he will not run for the position. Sources said last week that Barrasso intends to run.

“I do think I can make a contribution to the Senate in more valuable ways outside of the leadership,” Johanns told the newspaper. “Unequivocally, I am not seeking that post.”

Johanns, a first-term Senator considered a rising star in the Senate Republican Conference, declined to say who he might support for Conference Vice Chairman. The position ranks fifth out of the five top leadership positions, and does not carry much power.

“I don’t want a big campaign to start that I’m not a part of,” he said. “After November, I’ll see where the dust settles and make a personal decision about who I might support for the post.”

Senate Minority Leader Mitch McConnell (R-Ky.) does not intend to wade into the contest, according to GOP sources. Murkowski was projected to be a shoo-in for re-election until her defeat at the hands of Fairbanks attorney Joe Miller in Alaska’s GOP primary.