What does 'Me puede que....' mean?

[Danny T]

People on Twitter are saying things like "Me puede que escuche la música" and " Me puede que me digas que me amas". I just can't get the meaning in these contexts.

[Try My Best!]

Me puede que escuche la música = i can hear the music
Me puede que me digas que me amas = can you tell me that you love me

[Yossm]

it means "may i" as in may i do something for you .

[Jorge]

I am mexican and that sentences are wrong, so ignore them thats just bad spanish. it should be"puede que escuche la música" "puede que me digas que me amas"

[~Lau~]

it's not literal, it's an expression, it means "it's my soft spot that.." "I can't resist when..." "it break my defences that.." (ugh!! I can't give an exact translation!! but something like that). alone it doesn't mean anything "me puede que" doesn't mean anything alone, but in those contexts that's what it means

"me puede que escuche la música" doesn't mean anything, it's missing something, like that it means "it's my soft spot that he listens to the music" haha what?
but
"me puede que me digas que me amas" means "it's my soft spot that you tell me that you love me" aaww ^_^
like you just can't resist it and you succumb ^_^
like:
-Por favor!
-No quiero
-Te amo!
-Ay ^_^ me puede que me digas que me amas. Bueno, lo voy a hacer.
believe in me, I speak spanish, I'm from Argentina (maybe in other countries it doesn't mean the same, but here it does, I'm saying this because of the person of Mexico that answered above me, check out where the people who are tweeting it are from, maybe they are from Argentina)