Former Sen. Mark Begich is telling Alaska media outlets that he’s receiving encouragement to enter this year’s Senate race. 

“I’m getting a lot of calls from people who say they are not satisfied with their choices and they are not interested in seeing another Miller-Murkowski fight,” the Democrat said in a statement to the political blog The Midnight Sun. 

Republican Sen. Lisa Murkowski is running for re-election, having easily won her primary in August. In 2010, she was defeated in the primary by tea party-backed Joe Miller. But through a write-in campaign, she then defeated him in the general election. Last week, Miller announced he was running as the Libertarian candidate, setting up a rematch between himself and Murkowski. 

[Joe Miller Mounts General Election Challenge to Murkowski]

Begich did not offer a specific time table for deciding whether to run or not. “That decision I can make as, you know, as the time permits, but you know, the election isn’t until November,” Begich told KTVA Alaska in a phone interview on Tuesday from Washington, D.C. 

Murkowski told Roll Call that she viewed reports of a possible write-in Senate bid by Begich as “still in the category of interesting rumors.”

[Lisa Murkowski: From Write-In to Shoo-In?] 

Independent Margaret Stock and Democrat Ray Metcalfe are running in November. 

“I’m not supporting the Democratic nominee. I’ve said that publicly more than one once,” Begich told KTVA. “He has yet to show what he sees as the future of Alaska and what he can do and what he can bring forward, and that’s frustrating to me and frustrating to a lot of people.”

Begich lost his 2014 re-election to Sen. Dan Sullivan by 2 points — a race in which he tried to tie himself to Murkowski.

Since losing, he’s become a strategic adviser at Brownstein Hyatt Farber Schrek, advising the firm’s government relations department as an independent contractor. He also started his own consulting firm, Northern Compass Group. He splits his time between Washington and Alaska, he told Roll Call last year. 

Niels Lesniewski contributed to this report.