Twenty-nine-year-old Price won the titles in May with a fourth-round knockout of Sam Sexton in Aintree and will put them on the line against Harrison, 40, according to the Liverpool Echo newspaper.
Harrison (28-5), gold medallist at the Sydney Games in 2000, won the European title in 2010 and defeated Ali Adams in his last fight following a loss at the hands of David Haye.
Favourite Price (13-0) picked up bronze four years ago in Beijing and is tipped by many to surpass Harrison’s professional accomplishments.
Price’s promoter Frank Maloney is also expected to announce that the boxer will sign a deal to join subscription channel BoxNation for the next 12 months.
On the Price-Harrison undercard, Kevin Satchell will challenge Chris Edwards for the British flyweight title.