Arrieta, 31, spent the last four-plus seasons with the National League Central rival Chicago Cubs, emerging as one of MLB's best starting pitchers. He went 14-10 with a 3.53 ERA and 1.22 WHIP in 2017, his second straight season of statistical decline from his 2015 peak.
Teams like the Brewers will likely be encouraged by Arrieta's performance after the All-Star break, when he went 6-3 with a 2.28 ERA and 1.09 WHIP.
The Cubs have maintained they are open to bringing Arrieta back.
"We have never ruled anything out with him," president of baseball operations Theo Epstein said Friday, per Bruce Levine of CBS Chicago. "He earned the right to be a free agent. He gets the ability to talk with 30 teams. I am sure he has a number of suitors and this is a special time for him. He will take his time and find the right contract and right place. We wish him well. It is not that we have closed the door to him at all. We will just see where this offseason takes us."
Arrieta's agent, Scott Boras, is known to be patient with the market, waiting for the best offer. It would likely take a contract of five or six years to land Arrieta at this point, though spring training is nearing.
Moustakas, 29, hit .272/.314/.521 with 38 home runs and 85 RBI last season. He's spent his entire career with the Kansas City Royals, becoming an integral part of a core that ended the franchise's 28-year playoff drought.
The veteran third baseman is widely expected to be out of the Royals' price range.
The Brewers finished 86-76 in 2017. If they sign talents like Arrieta and Moustakas, it could be a signal they're going all-in to challenge the Cubs' hold on the top of the Central.