Brook will fight Australia’s Michael Zerafa on December 8 at the Sheffield Arena in a final eliminator for the WBA light-middleweight title.
But the action in the ring could be a sideshow to the sparks that fly afterwards, if Khan takes Brook up on his invite.
“I want to close the year in special fashion and set up some blockbuster fights in 2019,” said Brook, who beat Sergey Rabchenko inside two rounds in March.
“I was ringside for Amir Khan’s last fight, so let’s see if he’ll be there on December 8, or will he be too shook for Brook?”
Brook attended both of Khan’s comeback fights this year, entering the ring to trash-talk his longtime adversary in April.
Khan responded via Twitter: “All the crying you do, then u go and fight another bum. What’s the delay Kelly?
“Your (sic) a joke. Ps You better not lose in December! ‘I won’t be ringside!’”
The bout with Zerafa will be Brook’s second in the 154lb division but to fulfil his ambition of meeting Khan next year he will have to drop back down to 147lb, at which he was an IBF welterweight world champion just 18 months ago.
Before then, Brook – who was 36 fights unbeaten before losing to Gennady Golovkin and his title to Errol Spence Jr – must overcome Australia’s Zerafa.
Zerafa, 26, is a former Commonwealth super-welterweight champion and has secured 14 of his 25 wins via knockout. He has lost just two of his 27 professional fights.
Brook said: “This is the biggest opportunity of his career and he will be coming over here to take my scalp. But there’s levels in this game and I need to put him away to get the big fights I desire.”
Brook will be trained by former boxer John Fewkes because regular trainer Dominic Ingle has other commitments.