J Lo Has Not Returned Engagement Ring to A-Rod

J Lo and A-Rod may have broken up, but there are still some housekeeping matters to tend to .... notably, who gets the $1.8 million engagement ring?

Sources with direct knowledge tell TMZ ... JLo still has the ring in her possession. As you may know, an engagement ring legally is a "gift in contemplation of marriage." When the couple breaks up before hitting the alter, in most states the dude gets the ring back.

Our sources say there's been no discussion between JLo and A-Rod over the fate of the ring. However, our sources are quick to add ... the former couple exchanged "massive amounts of jewelry." A-Rod bedazzled JLo with all sorts of bling, and she fortified his massive watch collection.…