The word "can" is used for present possibility.
Can you jump as high as this?
Can you do my homework for me?
I can cook dinner, if you like.
Can you stay a while?
I can't sleep.
I can either study or watch television. I'm trying to decide.
Can you sign this for me?
Of course, there are cases where "can" would be unidiomatic and we use "may" ("I won't call him now - he may be asleep") or an adverb such as "perhaps".
Although "might" is technically a past tense modal, it can also be used to describe present possibility (as well as future, as you noted):
She might love me, but I don't know for sure.
He might be out shopping.
She might be at her desk. I'll check.
It might be raining. I'll look outside and see.
Isn't it working? It might need re-charging, or it might be broken.