The poll of the crucial Senate battleground state shows Begich is vulnerable. His approval rating is nearly even at 42 percent to 41 percent.
Alaska is one of four Democratic-held seats where the GOP has a good chance of knocking off the incumbent.
Palin, the 2008 Republican vice presidential nominee, has made noises about running but would have to give up a lucrative contract as a contributor to Fox News.
If she does run, Palin would lead the primary field with 36 percent support, the poll found. Treadwell has 26 percent support, Alaska Department of Natural Resources Commissioner Dan Sullivan (R) has 15 percent for 2010 Republican nominee Joe Miller has 12 percent.
With Palin taken out of the poll mix, Treadwell leads with 33 percent to 25 percent for Sullivan, who is seriously considering a run, and 24 percent for Miller.
The automated poll of 890 Alaska voters and oversample of 507 usual GOP primary voters was conducted from July 25-28. The main poll's margin of error is plus or minus 3.3 percent while the primary's margin of error is plus or minus 4.4 percent.