Want Cy Young winner R.A. Dickey to teach you how to throw a knuckleball? $10,000. (Read More: MLB Players Fear the 'Fiscal Cliff', Too!)
You can shoot hoops with former NBA stars like Tim Haraway or John Starks. They might even help out with a fantasy draft or just go out for dinner.
Starks is also available to play golf—for $5,000.
The possibilities may not be limitless, but they are greater than most fans and consumers previously had at their disposal.
"We sent a current Knick to a Bar Mitzvah," said Gerson, who admitted that "player" was J.R. Smith. Just a few days later, Smith sunk a game-winning shot.
"The player sees the 13-year old Bar Mitzvah boy, picks him up on his shoulders and brings him into the room. Everyone had a great time."
Even the athlete.
"When you look at athletes, in particular, they are brands," said Tiki Barber, who also goes out for flag football games and would even sing a little karaoke with you. "The problem is when they retire, they can't monetize it anymore 'cause the Giants or the Jets or the Knicks or the Dolphins or whomever aren't willing to pay for it any longer."
That's the key. The athletes choose the activity they want and then set a price. Thuzio tacks on a 20-percent premium to that.
Then, the consumer goes to the site, views the "menu" and can choose what he or she wants to do. All transactions are completed on the site.
"Here's a way for them to offer services that they think may be desirable to their consumers, and do it in a very easy straight forward way," Barber said.
Both Gerson and Barber learned that the athletes signed on with them want to interact with their fans. And for the average consumer with a little bit of money, there really isn't a service quite like this.
Sure there are sites like goviva.com, but they weave in a travel component.
Thuzio can send an NBA player to your son's bar Mitzvah!
If you want something less conventional, how about a swim lesson from gold medalist Chris Jacobs—a bargain at $200.
You could hang out with ex-heavyweight boxing champ Larry Holmes. He'll do just about anything—within reason, of course—for $6,250.
(Read More: Sports: It's a Tiger Woods Year.)
How about this?
Eat a hot dog (or 12) with competitive eating champ Kobayashi. That will cost $1,500—plus the hot dogs.
"You can come to the site, and you could say I'd like to have a meal with Kobayashi and do food photography, which is a real passion of his," said Gerson.
As for the business itself, Gerson can't be specific, but he can be optimistic.
"I don't know exactly how big it can be, but it can be enormous," he said.
The focus right now is around New York and Florida, but Gerson and Barber said it scales up easily, and they envision a global business that goes beyond sports.
They've even discussed the possibility of expanding to opera singers.
Right now, they have about 350 athletes signed on, and new ones join every day—from ultra-marathon stars to hockey players.
Eighty percent are ex-athletes, and although some critics think it's a money grab for the athlete, Thuzio said that's less accurate than you may think.
"I don't know the individual finances of any of the participants on our platform and what makes them financially want to participate," Gerson said. "But for current players and most retired players, one of the major reasons why they participate—and it comes up in every conversation we have with them—is that they genuinely enjoy this kind of engagement.
"It's harder for fans to engage directly with the players. It doesn't mean the players don't want to do it. The athletes do want to engage with their fans."
—By CNBC's Brian Shactman; Follow him on Twitter: