The actress, 34, was photographed wearing a large diamond ring on her left hand while in Los Angeles on Friday while she was running errands in a black T-shirt, jeans and a sweatshirt tied around her waist.
Representatives for Mara and Pheonix did not comment when asked about the pair's relationship.
Mara and Phoenix, 44, have been romantically linked since filming Mary Magdalene in late 2016. The two were reportedly seen spending time together on and off set while filming, including an outing on their Italian hotel's balcony where they were seen hanging out while smoking. They previously worked together on 2013's Her.
They made their red carpet debut at the 2017 Cannes Film Festival where they were seen chatting and warmly embracing when Phoenix won the best actor award for his performance in You Were Never Really Here.
"They were talking to one another nonstop," a source told People at the time. "Small talk between them. Then they went for their car and he's holding her hand like it was unconscious. Like it fits. They seem a totally natural and easy couple."
Phoenix previously dated his Inventing the Abbotts costar Liv Tyler from 1995 to 1998, and later model Topaz Page-Green in the early 2000s and DJ Allie Teilz. Mara dated director Charlie McDowell from 2010 to 2016.