09/08/2010 05:38 pm ET Updated May 25, 2011

Lisa Murkowski Likely To Run As A Write-In Candidate For Senate In Alaska, Fox News Reports

Sen. Lisa Murkowski -- who shocked the political establishment when she was defeated by Tea Party-backed candidate Joe Miler in Alaska's GOP Senate primary last month -- is likely to run as a write-in candidate to keep her reelection hopes alive, Fox News reports.

According to the network, sources familiar with the matter say Murkowski is expected to announce how she plans to conduct her campaign in coming days. If the Republican incumbent follows through in mounting an independent campaign, she would face-off against Miller once again, as well as Democratic candidate Scott McAdams to keep her seat.

A senior Republican leadership aide told Fox that should a three-way general election match-up arise, "The entire Republican leadership has endorsed and would continue to support Joe Miller."

On the heels of Murkowski's loss to Miller, Texas Sen. John Cornyn, who chairs the National Republican Senatorial Committee, signaled that he would firmly support the unlikely Senate nominee in Alaska's general election race.

"The NRSC is committed to doing everything that we can in order to ensure Joe Miller's victory this November," explained Cornyn. "I have no doubt that he will be elected as the next U.S. Senator from Alaska."

The AP reported earlier this week that Murkowski considers herself to be "still in [the] game.":

Murkowski told The Associated Press on Tuesday that she's been inundated with calls and e-mails from supporters and overwhelmed by people just coming up to her, asking her not to leave the race. She said she had been ready to consider her future outside the Senate on Aug. 31, when she conceded, but has been humbled by the outpouring from Alaskans, is listening and weighing her options.

She said that if this was "all about Lisa, certainly the easy thing for me to do would be to figure out what my next opportunity would be with my family and just settle in to a nice job."

"But what I'm looking at is my state and the future of my state for my kids. So, I have not made that determination that I'm going to give up. I'm not a quitter, never have been. And I'm still in this game," Murkowski said.