Schaefer was speaking at the announcement of a long-term deal that will see BoxNation screen two live GBP shows per month, including Mayweather's May 5 superfight against Miguel Cotto.
Two weeks after Mayweather and Cotto collide, all attention will turn to Khan's potentially-explosive rematch against Lamont Peterson.
The first fight saw Khan relieved of his WBA and IBF belts in controversial circumstances with referee Jo Cooper deducting him two points for pushing.
At times the 25-year-old was happy to trade with the more rugged Peterson and Schaefer believes he would be better served by relying on skill over brawn.
"I don't know how to say it more elegantly, but sometimes Amir's balls are too big for his own good," he said.
"Look at Mayweather - he's a master tactician who knows how to use defensive and offensive skills and has been knocking people out recently.
"He knows what it takes to win and fights very smart.
"Amir has the skills, speed and power, but what he needs to work on are the 'ring smarts' and not get carried away.
"He's still very young and he learnt a lot from the Peterson fight. We'll see if he applies that on May 19."
If Khan dispatches Peterson and Mayweather disposes of Cotto, Schaefer believes the rivals could meet early next year.
However, he would like to see Khan step up a division and have one fight at welterweight before locking horns with Mayweather.
"There's never going to be a boring Amir Khan fight because he is incapable of producing that," Schaefer added.
"He's an exciting guy to watch and that's why we all want to see him."
Schaefer remains convinced Mayweather and rival pound-for-pound contender Manny Pacquiao will eventually clash in what could be the richest fight in boxing history.
"It will happen but not this year, probably when Pacquiao is ready to retire and has run out of other options," Schaefer said.
BoxNation's tie-in with GBP commences on April 21 with a double world-title show of Abner Mares v Erik Morel for the vacant WBC world super-bantamweight title and the WBA world super-bantamweight title clash between Anselmo Moreno and David De La Mora.
A week later Bernard Hopkins' rematch with Chad Dawson for the WBC world light-heavyweight title will be screened.
The agreement excludes any Mayweather fights after May 5, although BoxNation owner Frank Warren confirmed they will bid for any contest in which the 35-year-old is involved.
"If Mayweather fights Manny Pacquiao I can assure you we'll be in for it," Warren said.