Eli Manning -- Something's Fishy About Tom Brady's Ball Habits

Eli Manning claims he doesn't give a crap about the pressure in his footballs -- and says the fact that Tom Brady obsesses over it seems incredibly strange to him ... and TMZ Sports has the footage.

The 2-time Super Bowl champ was a guest speaker at a private function at the New York Athletic Club last week when he was asked for his opinion on Deflate-Gate.

"I never worried really much about the inflation," Manning said ... "I thought it was kind of strange that [Tom] Brady knew he liked his ball at 12.5 pounds of pressure in the ball."

"That's the minimum number you can have ... seems kind of strange to me."

But get this, Manning says he's not convinced the pressure in the ball "is that big of a deal" ... and claims the Brady scandal is the first he's ever heard of an issue with inflation.

Manning -- who seems to be the bane of New England's existence when it comes to Super Bowls -- also told the crowd what he thinks could be the key to another Seattle victory.