Former Alaska Senate nominee Joe Miller (R) stopped by Sen. Mark Begich's (D-Alaska) office on Thursday to thank him for nominating his son to a military academy — but wouldn't say whether he'll run against Begich this election.

The Tea Party favorite defeated Sen. Lisa Murkowski (R-Alaska) in a 2010 GOP primary, but Murkowski stormed back to win the general election as a write-in candidate. Now Miller is mulling a run against Begich, who's up for reelection.

"You never know who will stop by the office," Begich wrote on a Facebook post accompanying a picture of the two.

Begich, running in the heavily Republican state, could be a top GOP target this cycle. But if Miller wins the Republican nomination, the senator would likely be in much better shape, as Miller is seen by many in Alaska as outside the mainstream.

Murkowski and Rep. Don Young (R-Alaska) also backed Miller's son for the academy, and he stopped by to thank them as well. A Murkowski spokesman said the two had a "friendly Alaska conversation."