The two fighters have been feuding for a while now, with speculation growing about the duo squaring off in the ring in 2013.
Despite losing to Price twice in their amateur career days, Hennessy believes that Fury will easily defeat the 29-year-old.
"If David Price really genuinely wants to fight we will put our world title plans on hold and we will make the fight," said Hennessy.
"When it comes down to it, that is a fight that Tyson will look absolutely sensational in and he'll take David Price apart.
"[Price is] nowhere near a world title. He may be almost six years older than Tyson but he's a novice compared to Tyson."
Fury's last victory came as he beat Vinny Maddalone to claim the vacant WBO Inter-Continental Heavyweight title.