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May 27, 2015 12:00 PM

Are Katy Perry and John Mayer back on again – or have they simply bonded platonically over a shared appreciation for Space Mountain?

The famously on-and-off couple were spotted at Disneyland Monday, wearing oversize hooded jackets and attempting to keep a low profile as they enjoyed the theme park.

The nature of the relationship between the “Who You Love” singers has been a source of speculation for months, with one source telling PEOPLE the pair are casually dating at most.

“They have spent time together, but it doesn’t seem like they are back in a serious relationship,” says the source. “It seems they only see each other whenever it’s convenient. They have spent time in L.A. when Katy has had a break from her tour. They hang out at Katy’s house and have had a dinner date at Sunset Tower.”

Perry, 30, and Mayer, 37, first started dating in the summer of 2012 and weathered a couple of breakups before what appeared to be a final split in February 2014.

The couple fueled rumors that they had rekindled their romance back in January of this year after they were seen out together in Beverly Hills. However, as a source told PEOPLE at the time, “They actually buried the hatchet a while back, and they are friends. It’s not a surprise they would see each other socially. She’s focused on her career and making herself happy.”

A short time later, the duo were spotted hanging out with Missy Elliott after Perry’s successful Super Bowl halftime show.

RELATED VIDEO: Why Did Katy Perry’s Halftime Performance Remind Us of Spongebob?

Perry’s former relationship woes recently made headlines when Sydney’s The Daily Telegraph resurfaced an interview conducted three years ago and “stamp[ed] a new date on it,” as Perry later criticized on Twitter.

That said, the old quotes still appear relevant today. When asked whether she felt any “trepidations” when it comes to falling in love again following her split from ex-husband Russell Brand, she said: “No, absolutely not. I’m excited by whatever it brings. I’m excited by my own evolution.”

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