The NFL is looking into the matter, league spokesman Michael Signora confirmed to ABC News this morning.
Deflated balls may be more difficult or easier to catch, depending on how much air is missing.
This morning, Brady called the suggestion “ridiculous” during an interview on WEEI radio in Boston.
"I think I've heard it all at this point ... it's ridiculous," Brady said. "I don't even respond to stuff like this."
The NFL’s guidelines dictate that a ball must be inflated to about 12.5 and 13.5 pounds per square inch and weigh between 14 and 15 ounces.
"Officials check balls as they go into the game, and if the ball doesn't feel perfect, they can throw it out," former NFL official Jim Daopolous told ESPN. "There is always the possibility that balls can lose air due to the conditions."
The news broke when a columnist with WTHR in Indianapolis said a league source had told him the NFL was investigating the matter.
The minimum disciplinary action for anyone, including the head coach or other club personnel, who is responsible for a non-approved football is a fine of $25,000, according to the NFL's game operations manual.
In 2007, NFL commissioner Robert Goodell fined Patriots coach Bill Belichick $500,000 and the team $250,000 for recording the New York Jets' defensive signals. The Patriots were also stripped of their first-round draft pick.