Boston Red Sox Shoot Shot with Jennifer Lopez, If Ben Affleck Can Get Her Back ...

With Ben Affleck back in the picture, the Boston Red Sox clearly see an opportunity to land a huge (possible) free agent ... Jennifer Lopez!

Yeah, we know ... Jenny's from the Bronx, but since she split with A-Rod, it's hard to see her rooting for the Yankees any time soon.

Plus, the NY Mets rejected her offer to buy the team a few months ago -- guessing she ain't supporting them either.

So, leave it to Boston to make a move to win over one of the most famous celebs in the world ... and they might have a real shot!

The Red Sox posted a video to TikTok reflecting on the time J Lo took in a game at Fenway Park back in 2019 -- when the Sox played the visiting L.A. Dodgers.

A-Rod was working the booth for ESPN that night -- and while he was distracted, seems Jennifer really hit it off with the Red Sox mascot, Wally!

Now, with Lopez spending some quality time with Affleck -- one of the most diehard Boston fans on the planet -- the Red Sox are hoping she'll join him back at the Park the next time he catches a game in person.

"To the girl on the Monster from Sunday Night Baseball in 2019, We will never forget you," the Red Sox posted ... "Come back soon. We miss you."