According to multiple outlets, the Coldplay singer popped the question to the actress a while back ... although it's unclear exactly when he might've gotten on bended knee. Some reports suggest he might've popped the question as far back as 2020, if not earlier.

These same reports go on to suggest the couple are in no rush to get hitched -- doesn't sound like there's any concrete plan on setting a date and saying 'I do.' So, they're chillin'.

One report even goes so far as to suggest that Chris' ex-wife, Gwyneth Paltrow, is fully on board with them getting married ... which jibes with how she and Dakota interact in public ... they're pretty chummy.

Of course, Dakota's also been playing stepmom to Chris and Gwyneth's two kids, Apple, 19, and son Moses, 17 -- and GP's even been super open about how their love for their kids keeps their co-parenting relationship strong post-divorce, which came two years after their "conscious uncoupling" back in 2014.

As for Chris and Dakota, they've been linked since 2017, with a brief bump in the road in 2019, when they briefly split. They got back together, of course, and have been happily dating ever since ... but with this new update, it seems they've been fiancé/fiancée to one another.

Dakota might've been telegraphing this all along she's been spotted bling on her ring finger in recent years -- and some reports suggest that it was an engagement ring after all.