Despite several attempts over the years – and plenty of call-outs and trash talk – a bout between the pair has never come to fruition.
Khan claimed on Sky Sports that he has contacted Eddie Hearn but has not received a “clear response” from Brook’s team they want to accept his offer.
He said: “Now is the right time to make that fight happen with Kell. We both have been world champions. We're both British and in the north as well. Imagine making a huge fight like that happen at the Old Trafford football stadium. It would be a massive fight.
"It will be good for boxing, especially to settle the score and put him in his place."
Brook's most recent bout was a fourth-round stoppage loss to WBO welterweight champion Terence Crawford in November, while Khan has been absent from the ring since a victory over Billy Dib in July 2019.
The Sheffield fighter, now 34, was not promoted by Matchroom Boxing’s Eddie Hearn in his last fight and did not work with long-standing trainer Dom Ingle.
“I’m not running away from that fight, I’ve got his number,” Brook previously told Sky Sports.
“We’re both at the stage of our careers now where we can lock horns and get it on.
“I believe it can happen, the fans need to see this fight.”
Brook is yet to respond publicly to the latest call-out.