We talked to Jonathan about Brees opening a special needs playground in NOLA ... and Jonathan went full campaign manager describing his longtime teammate's mayoral credentials.

"He definitely has a future as mayor of New Orleans," Vilma told TMZ Sports.

"Drew Brees was the best teammate I had. Words can't describe how competitive he is, was, still is, to what a great person he is."

"So every time I see something come out on him doing something off the field that's positive ... it's par for the course."

The question -- is Drew actually gonna do it??

We asked him earlier this year ... and he definitely didn't rule it out.