Mahomes clinched his second Super Bowl ring as he led the Chiefs back from ten points down at half-time, throwing three touchdowns as his team defeated the Philadelphia Eagles 38-35 on Sundayagles.
The 27-year-old joins Tom Brady, Joe Montana, Eli Manning and Terry Bradshaw as quarterbacks who have won two Most Valuable Player (MVP) awards in a Super Bowl.
But Reid suggested that Mahomes, whose father Pat was a professional baseball player, has his sights set even higher.
"He grew up in a locker-room and he has seen the greats and he strives to be the greatest. Without (him) saying anything, that is the way he works. He wants to be the greatest player ever, that is what he wants to do and he goes about his business and does it humbly," said Reid.
Mahomes became only the 13th starting quarterback to win more than one Super Bowl rings. He also became the 11th player to win the Super Bowl and league MVP in the same season and the first to do so since 1999.
The 64-year-old Reid said that after they left the field he had told Mahomes how much he appreciated his approach.
"I told him I love him, I am proud of him for leading the way there. He is a humble kid and works his tail off and as a coach you respect everything that he does there," he said.
Mahomes completed 21 of 27 passes, throwing for three touchdowns, 182 yards and no interceptions.
Reid said those kind of numbers, like others he has produced in his career, could go to a player's head but not in the case of the Texan.
"There is no bragging. He could stand here and give you the stats he has that are incredible but he doesn't do that," he said, noting that he has an ability that cannot be quantified in numbers.
"When it is time for the guys around him to raise their game he helps them with that. The great quarterback make everyone around them better, including the head coach," he added.
"He has done a heck of a job."
Mahomes has battled against the pain of an ankle injury throughout the post-season, including the Super Bowl and his team-mate, tight-end Travis Kelce, said he had shown his fortitude.
"Toughest son of gun you ever met man. That Texas gunslinger ain’t going to let nothing get in the way," he said.
INJURY CONCERNS
Mahomes had limped off the field wincing in pain after their final possession of the first half, heading into the locker room with the Eagles up by 10 points as Chiefs fans worried he had exacerbated an ankle sprain suffered earlier in the postseason.
"I felt really good until I reaggravated it a little bit," Mahomes told reporters. "You're in the Super Bowl - you can worry about getting it healthy in the off-season. So I fought through."
He showed he still had the magic touch after the break, engineering an extraordinary comeback by throwing two touchdown passes and scrambling 26 yards late in the fourth quarter.
"I knew it was pretty bad when he got up limping," Chiefs offensive coordinator Eric Bieniemy told reporters.
"But I knew it wasn’t going to be bad enough where he pulled himself off the field. That’s just Pat; that’s who he is since Day 1.
"He is as competitive as they come and he’s not going to ever pull himself out of a situation with his team, through the good and the bad."
Alongside being named MVP, he became only the second player to throw for more than 5,000 yards and 40 touchdowns in multiple seasons after producing a career-best 5,250 passing yards.
"Pat is a once and generational lifetime type of player and sometimes he does things so special that becomes normality for him," said Chiefs defensive tackle Chris Jones.
"We’ve got to just appreciate Pat."
