The 29-year-old heavyweight has his sights set on a world title and his promoter believes that further exposure across the Atlantic will further enhance his burgeoning reputation.
Thompson, 41, suffered just the third loss of his 36-fight career when he clashed with Wladimir Klitschko in July.
"It's a great fight," Maloney told Sky Sports News. "Price is well established in America. His last two fights will be shown on TV over there and this will be too. Price has caught the public's imagination.
"People said his career was going nowhere but I believe we have an art in developing heavyweights. He's the most successful Olympian from 2008."
Maloney further fuelled speculation of a potential bout with domestic rival Tyson Fury, which has become one of British boxing's longest-running war of words.
"Will the fight happen? It should do for the public," Maloney added. "We're willing to sit down and negotiate. If Mick Hennessy wants me to apologise for my remarks about Tyson Fury and that'll help make the fight, then I apologise.
"If you don't want to fight, be honest. Dealing with Mick Hennessy is like a reincarnation of Rock Newman and Riddick Bowe. They don't want the fight and I don't blame because they'd get beaten and they wouldn't the chance to fight for a world title.
"Maybe David will let him fight for his world title once he becomes champion."
Price disposed of Matt Skelton in the second round of their meeting at the start of the month.