Hughie Fury is avoided by the biggest names in the heavyweight division but will continue pursuing "a big fight" to tee up a world title chance, says promoter Ben Shalom.
Chris Arreola and Trevor Bryan's names are "in the hat" as a possible opponent for Fury's next fight, which is pencilled in for February.
Derek Chisora, who will first rematch Joseph Parker next month, is a preferred target for Fury in 2022.
"There is a lot of interest in fighting Hughie from heavyweights stateside so he will have a lot of options," BOXXER promoter Shalom told Sky Sports.
"But we have offered him out to a few of the bigger names. But Hughie isn't someone they want to fight.
"He is very young and very awkward - the experienced heavyweights know to avoid him.
"So we have to choose carefully who he should fight to position him well for a world title shot."
The younger cousin of the WBC heavyweight champion Tyson Fury delivered his most spiteful performance to date in his most recent win, stopping the durable Christian Hammer in five rounds.
"I had more gears to offer," Fury told Sky Sports afterwards.
"He was getting sick in there."
Fury is ranked at No 4 by the WBA whose 'regular' belt is held by American Trevor Bryan, who is undefeated in 21 fights.
Chris Arreola, who has shared the ring with Vitali Klitschko and Deontay Wilder, is coming off a spirited performance against Andy Ruiz Jr where he scored a knock-down before being outpointed.
Fury's only defeats came against the seasoned trio of Joseph Parker, Kubrat Pulev and Alexander Povetkin, but he is still only 27 and has beaten veteran duo Hammer and Mariusz Wach consecutively.
His father and trainer Peter Fury previously warned: "He's been ahead of his time. He fought for a world title aged 22.
"You can't put men against young men or boys. Now, he's arrived on the scene as a full-set man.
"They are in the fight business. They are brought up street-fighting. It's a no-surrender business, it's not play.
"He'll fight until every last drop of blood leaves his body. The only time he goes out is if he's out cold.
"This is a warrior sport."