What's really going on with Armie Hammer and Rumer Willis?

Is Armie Hammer calling Rumer Willis by her name? On Sep. 3, 2020, the two stars were spotted out and about together in Los Angeles, looking cozy — quite cozy in fact — "walking arm in arm," according to Entertainment Tonight. In photos obtained by Page Sixthe Call Me By Your Name star looks cool and casual in a loose hooded sweatshirt and slacks. Willis — actress, singer, and daughter of Demi Moore and Bruce Willis — wears a striped sweater and white pants. Both are quarantine-friendly, wearing masks to ostensibly keep safe amidst the COVID-19 outbreak.

Rumer and Armie's hangout comes just two months after he and food entrepreneur Elizabeth Chambers announced their separation. Fresh off celebrating their tenth anniversary, the couple, who share two children together, Harpur and Ford, announced their divorce on July 10, 2020. Rumer has never been married. 

"Thirteen years as best friends, soulmates, partners and then parents," Hammer and Chambers posted on their Instagram accounts. "It has been an incredible journey, but together, we've decided to turn the page and move on from our marriage. As we enter into this next chapter, our children and relationship as co-parents and dear friends will remain our priority." 

Keep reading for more details on the intriguing dynamic between Armie Hammer and Rumer Willis. 

Both Armie Hammer and Rumer Willis have been busy

So what's the deal with Armie Hammer and Rumer Willis? Nothing's official yet, but Willis did comment on one of Hammer's Instagram posts with an emoji (a.k.a. flirting), per the Daily Mail. Otherwise, the superstar daughter and A-list actor have been plenty busy pursuing individual interests.

Hammer has apparently been hunkered down with a close friend amidst his divorce from Elizabeth Chambers. According to Entertainment Tonight, the actor even celebrated his birthday exclusively with this pal and a nature hike. "This one of my best friends, Ashton. For the last 2 months or so I have lived with Ashton, worked construction with Ashton, and hiked with Ashton every day," Hammer posted to Instagram in late August, 2020. Meanwhile, Hammer's children are starting school with their mom on the Cayman Islands, People reportedThough the family is apart, Hammer seems...better. Earlier in the summer, pre-split, he worried fans by shaving his head and posting strange videos of him chugging beer. (Well, everyone handles quarantine differently.)

Meanwhile, Willis recently made waves participating in Kim Kardashian's SKIMS shapewear campaign, posing in multiple revealing posts on her Instagram Page and looking uncannily like the line's creator, according to Us Weekly. Willis' involvement coincided with the brand's one-year anniversary. "Happy Birthday @skims!!! Thank you to the team and the oh so lovely @kimkardashian for including me. You are a gem my dear," Willis captioned one post. Maybe Armie saw those pics and gave Rumer a call!