Patriots quarterback Brady is a five-time NFL Super Bowl champion after helping New England beat the Atlanta Falcons in Super Bowl LI last month.
Messi, meanwhile, is a five-time Ballon d'Or winner among his 27 trophies for Spanish and European giants Barcelona.
Gronkowski attended Barca training on Thursday, having watched Messi's men rout Sporting Gijon 6-1 on Wednesday and the Patriots tight end was starstruck.
"I'm going to have to go with Messi," the 27-year-old American said after being asked to name his favourite player. "I just met him, and he was super cool.
"I'm a huge fan [of Barcelona] now."
But when asked to compare Messi to Brady, there was only one winner.
"Brady all the way," said Gronkowski, who is a two-time Super Bowl champion and four-time Pro Bowler. "He's the man."