The Boston Red Sox are holding out hope for Alex Bregman, and the latest Alex Cora tweet has fans speculating like never ...

Red Sox manager Alex Cora took to social media on Monday night ... it's full of fan-edited images of Bregman wearing a Red Sox jersey or images of the All-Star with the Houston Astros.

It has been a struggle to push a big-ticket free agent signing across the finish line, but Boston has also been purposefully patient — especially when it comes to third baseman Alex Bregman ...