Jones, who was born in Charlotte and raised as a Carolina Panthers fan, told ESPN's Jordan Raanan that his first memory of the Patriots quarterback is New England's Super Bowl championship over his hometown team in 2004.
"I remember where I watched it," Jones told Raanan. "(We) went to a friend's house. The Dickens' house. A family friend. Obviously it was heartbreaking when (Patriots kicker Adam) Vinatieri made that field goal."
The New York Giants passer was only 6 years old at the time and said he didn't have particularly negative feelings about Brady, adding, "(I) don't think I knew that much at that age."
Jones said, "(I) grew up watching him. Obviously he's won a lot, achieved a lot in his career. So a lot of respect for that."
The six-time Super Bowl champion is 20 years older than Jones and won his first title when the rookie was 4.
New England looks to continue its undefeated season on Thursday against the Giants, who currently sit third in the NFC East at 2-3.