Faris first addressed engagement rumours while out and about in Los Angeles with Barrett whom she has been dating for two years.
When photographers asked how the couple are, she replied: "We're wonderful."
"Congratulations!" the paparazzi later added.
"Thank you," the actress responded, hinting that there may well be a wedding in the works.
Rumours of their engagement first graced Hollywood earlier this month when the 42-year-old was photographed wearing a diamond ring on her left hand.
The pair started dating in October 2017, two months after Faris' highly-publicised divorce from Chris Pratt.
Faris recently opened up about her notoriously private relationship with the cinematographer in a new episode of podcast Anna Faris Is Unqualified.
Speaking about her past marriages to Chris Pratt (2009-2018) and Ben Indra (2004-2008), the actress revealed: "This is a tricky area for me because I've gone through two divorces now."
"I'm in an amazing relationship, I do want to talk to everybody about these things, that I don't really know much about," Faris continued. "But I also feel that I want to protect things in a way that I hadn't considered before."
In June, Pratt married Katherine Schwarzenegger after announcing their engagement via Instagram in January.
Revealing the happy news on the social media platform, he wrote: "Sweet Katherine, so happy you said yes! I'm thrilled to be marrying you. Proud to live boldly in faith with you. Here we go!"
Proving there is no bad blood between her and Pratt, Faris swiftly congratulated the couple.
"I'm so happy for you both!! Congratulations!" she commented.