Looking on the internet deeply has found these results:

I may be available is the most popular phrase on the web.

I might be available 1645,000 results on the web	I may be available 117,300,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Adequate lighting facilities shall be available. I heard you're hiring on men. Well, I might just be available. Detailed plans shall be available for emergency vaccination. I might not be available then and, anyway, he needs help now. I might not be available, so I've given them your number. Information concerning source, preparation date and stability should be available. PHARE funding continues to be available. If you're here to invite me to the Lise Meitner dance, I might still be available.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I might be available

1645,000 results on the web

I may be available

117,300,000 results on the web

More popular!

Adequate lighting facilities shall be available.
I heard you're hiring on men. Well, I might just be available.
Detailed plans shall be available for emergency vaccination.
I might not be available then and, anyway, he needs help now.
I might not be available, so I've given them your number.
Information concerning source, preparation date and stability should be available.
PHARE funding continues to be available.
If you're here to invite me to the Lise Meitner dance, I might still be available.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.