Both are equally correct. "Mentioning" sounds a little more casual, but in this case, both sentences sound casual because of the expression "drop an email," which implies something quick and simple. In both sentences, it sounds like the report itself is important (we "need" it), but there's no feeling of urgency or anxiety in the writer's tone. Personally, I would probably choose "mentioning." Both are fine, though.

In corporate America it is typical to say "please ping (email, instant message) John to remind him we need the report by the end of day tomorrow." If you are talking third person you would say "I will see John at the 2pm meeting and will remind him that we need the report by end of day tomorrow." In corporate America, it is implied that if you need to mention (remind someone) then there is an urgency to the request.