A-Rod's Hamptons Summer Rental is Close to J Lo, but Not J Lo-Related

Alex Rodriguez is in close proximity to his ex, Jennifer Lopez, this summer -- but potential face time with her wasn't his intention when he signed the lease ... TMZ has learned.

Sources close to A-Rod tell us ... his $200k/month rental in the Hamptons -- is all about shortening his commute and getting R&R. Yeah, they're about a mile or so from each other, but we're told that's more coincidence, than convenience.

In case you hadn't heard, Alex will be chilling in this beautiful fortress of a house in a very exclusive 'hood -- yes, even for the Hamptons -- in a gated community, and features all the bells of whistles of luxury. Seriously, it's a palace.

There are 7 bedrooms, 4 baths, a movie room, a game room, pool and spa, a waterfall and yeah ... it's overlooking the water nearby. Also, he is indeed about 3 minutes from Jen's own Hamptons home in town.

While some have theorized A-Rod was trying to cozy up to J Lo -- maybe to try rekindling their romance -- our sources say his summer pad is great for his ESPN gig, calling Sunday Night Baseball games.

Every week he has to be in-studio in Bristol, CT ... which is way easier commute to from the Hamptons than Miami. Also, we're told he's got buddies in the Hamptons, including his T-Wolves co-owner, Marc Lore. Fact is, it's just where celebs and rich folks go every summer.