The singer posted a photo Sunday of a massive diamond ring that she says her boyfriend, Alexander Edwards, gifted her for Christmas -- and while it could certainly go on any finger ... there's a lot of speculation this might belong on THAT finger.

Unfortunately, Cher isn't giving a lot of hints here. All she wrote was, "THERE R NO WORDS, ALEXANDER,A.E." She then noted those are his hands holding the box.

Of course, the internet is flipping out over the fact Cher may be engaged again. She hasn't been married since Gregg Allman way back in the mid-to-late '70s, and obviously Sonny Bono before that. She's dated a lot of people since then ... including some pretty famous men like Gene Simmons, Tom Cruise, Val Kilmer, Richie Sambora, Warren Beatty and others.

None of those relationships ever got to the point of marriage though ... and if she is, in fact, set to walk down the aisle with AE, it'd be pretty stunning -- especially since they've only been dating for a handful of months now.

Although we know they met in September, they only went public as a couple a month and change ago ... so a would-be proposal is clearly moving things along quickly, if that's what's actually going on. Then again, this could simply be a regular diamond ring ... right?