Although the couple announced their split in December 2016 and Murray moved out of Stanton's California home, Murray revealed to Entertainment Tonight there's a chance of a reconciliation.
"You know, we're trying to deal with stuff in a more private manner now, obviously, and we just kind of want people to respect that, especially because it's a tough situation with the kids, and we don't want to kind of fully dive into anything, because we're thinking about them as well," Murray toldET, referencing Stanton's little girls Charlie and Kinsley from her previous marriage to Nick Buonfiglio.
Rumors of a possible rekindled romance surfaced this past weekend when Stanton and the former pro baseball player were spotted kissing and embracing in Los Angeles on Sunday.
The pair was photographed looking happy and in love in public, which came as a big surprise to fans considering Murray and the single mom weren't even on speaking terms last month.
"This is the first time I've seen her in a while," Murray explained of the outing.
"When I came out this week, I came for one of my friend's events, and I did some other stuff while I was here, and we ran into each other and stuff. You know, we just had long conversations. They were conversations that needed to be had, and [we had] a great dinner and everything like that... It was a good evening. We had a good time."
Murray proposed to the blonde beauty on Bachelor in Paradise's finale in Summer 2016 and left his hometown of Atlanta, GA, to be with her shortly afterwards. When the couple called off its engagement and conducted separate media interviews, it became clear they were just very different people who had trouble getting along.
"Whenever we're together, especially outside of the show and outside all the drama, it's always been a good relationship," Murray revealed to ET. "There were just so many outside forces and outside factors that got involved after we were together on the show, and it was unfortunate for a little bit."
For starters, Stanton was constantly warned by friends in the Bachelor franchise -- including Nick Viall -- that Murray had an ugly side. The allegations seemed to derive from his ex Andi Dorfman, who wrote in her It's Not Okay memoir that Murray had been jealous and verbally abusive in their short-lived romance following The Bachelorette's tenth season. (Dorfman and Murray split in January 2015 after several months together).
Murray and Stanton therefore seemed to spend a lot of time defending their relationship and trying to prove people wrong.
"We went through a lot," Murray said without getting into specifics. "We went through a lot more than people understand."
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Murray -- who admitted he's single as of now, having fun and meeting new people -- said the current state of his relationship with Stanton is "tough" but "there's a possibility for anything," including a reconciliation.
"It's tough going into detail about it. Like I said, I don't like talking about my relationships unless everything is great and there's positive things to be said, and there are positive things to be said of course, but there's a lot of things that we still need to talk about, just for moving on as friends or anything in the future, and we're beginning to do that," Murray elaborated.
"This week was good, seeing each other, so we could engage in good conversation, and we could talk about the things in the past and be mature individuals and adults. And that's what you do, you talk about things. Everything, as of right now, is fine."
Murray is looking forward to marriage and having children, but he's also "not going to settle" because he desires a partner with whom he truly wants to spend the rest of his life and does not want to get divorced.