There's a tutorial on drag & drop in this old thread:
viewtopic.php?p=249895#p249895
It still works if you make some very minor edits.

In 2022 this thread is still a top google hit for "love2d mouse drag", so for anyone trying to use this... The author's original writeup is findable here: https://web.archive.org/web/20201125055954/http://nova-fusion.com/2011/09/06/mouse-dragging-in-love2d/ and his original code is here: h...