Their unhealthy disregard for each other could be a lucrative selling-point for a Brook v Crawford clash in England this year - something the American's promoter is keen on.
Brook was criticised by Crawford some time ago - and that will have rankled the Sheffield man.
And Brook looked uncomfortable when he was unexpectedly harangued during a media interview filmed just after Crawford stopped Khan at Madison Square Garden last month.
In an awkward exchange, Crawford's sister said the South Yorkshireman was "too little" to get in the ring with her younger sibling and suggested Brook wouldn't want the fight anyway.
Brook acted with as much composure as possible given the circumstances and said he'd do a better job against WBO welterweight title holder Crawford than Khan did - the Bolton man was TKO'd in six rounds.
Brook suggested Khan hadn't wanted the fight, just the pay day, he was there "to lay down."
If he got in with Crawford: "I would show you a competitive fight - I'd show you I want to rip that title away from him. I'd want to win that fight" he told FightHype.com
Crawford's promoter Bob Arum sees sense in arranging a fight in England, rather than the US.
That's because British boxing fans turn up in numbers for such an event - while Crawford, 31, does not enjoy a huge fan US base despite his pound-for-pound credentials.
Brook is fed up to the back teeth of waiting for Khan, and sees Crawford as a huge opportunity to regain his status and prolong his career.
It would be an incredibly difficult task to get down to 147 pounds for Brook, who has just turned 33 years old.
But he would be confident of making that weight with such a mouth-watering contest on the horizon. And a win would put him on course to pay per view combat with likes of two boxers he'd love to fight again: Shawn Porter and Errol Spence Jr.
Matchroom's Eddie Hearn has said little definite about Brook since his last fight against Michael Zerafa at Sheffield Arena in December.
But he will be aware that the clock is ticking on Brook's career - and the fighter will want a memorable swansong either this year or in 2020.