Hi Alexey, Both are OK to say, however the first is proper English (for when you're writing an essay or letter), whereas the second is relaxed (spoken) English.

Sir, the first variant is more correct. I suggest, "Can I ask you for a favor" or "May I ask you for a favor?" The second variant can be adjusted to "Can I ask a favor of you?" When said this way, it is no more "relaxed" than the first option. Keep in mind, this is not Mr. Bean or Hugh Grant English; this is 100% Elvis Presley and Marilyn Monroe English.