AceShowbiz - Armie Hammer recently sparked rumors that he's currently dating Rumer Willis after their PDA-filled outing. Now, it's been reported that the "Call Me by Your Name" actor and the 32-year-old actress are not seriously dating just yet as both of them want to take their time for now.

Entertainment Tonight claimed that Armie and Rummer met through mutual friends and described their relationship as "very casual." A source told the gossip site that the two are now simply enjoying each other's company as Armie allegedly wanted to respect his ex-wife Elizabeth Chambers and would like to avoid hurting her feelings.

Rumors of their romance first sparked earlier this week after the two were spotted getting cozy while enjoying a stroll in Los Angeles. Sporting casual look in a drawstring top, brown pants and white sneakers, the "On the Basis of Sex" actor was pictured at one point wrapping his arm around the eldest daughter of Bruce Willis and Demi Moore as they headed to the Dialog Cafe in West Hollywood, California.

According to a source, Armie and Rummer enjoyed their meal for an hour before heading back. "They seemed happy and very familiar with one another," so the insider said. "They blended in with their masks on, and had their arms around each other closely while walking."

Armie was previously in a 10-year marriage to Elizabeth, with whom he shares two children together. The exes announced their split earlier this year through a joint statement. "Thirteen years as best friends, soulmates, partners and then parents. It has been an incredible journey, but together, we've decided to turn the page and move on from our marriage," so the statement read.

The statement continued, "As we enter into this next chapter, our children and relationship as co-parents and dear friends will remain our priority. We understand this news lends itself to public dialogue, but in the interest of our children and our family, we’re asking for privacy, compassion and love during this time."