Former Olympic champion Harrison knocked out of Ali Adams in four rounds on Saturday in his first fight since losing to David Haye in 2010.
The 40-year-old extended his record to 28 victories from 33 contests and said afterwards that he wanted to fight fellow Olympian Price or Tyson Fury.
And Harrison, who won gold in in Sydney 12 years ago, could now be in line to face 2008 bronze medal winner Price.
"It's a fight we're interested in," promoter Maloney told West London Sport. "We're looking to get in contact with him.
"There are a number of options we're looking at and I can say that Audley Harrison is one of them."
Price stopped Sam Sexton in four rounds earlier this month to extend his run to 13 wins after Fury opted to vacate both titles instead of facing his mandatory challenger.