The Norfolk side have offered around £2million for the 32-goal former Sheffield United man, and are in competition with Wolves and Sheffield Wednesday for the signature of Britain's top goalscorer.
Scunthorpe Chairman Steve Wharton confirmed that talks between Sharp and the powers that be have begun, although the Iron will be looking for a higher final bid before parting with their prized asset prior to the start of their inaugural Championship season.
"Norwich have had a £2m bid on the table for some time and want to be sure Billy wants to join them before pursuing their interest further," said Wharton. "They have offered £2m but they know we are looking for add-ons to that which could take the price to near the £3m mark if they are promoted to the Premiership.
"We have had increased bids from both Wolves and Sheffield Wednesday but neither of those come anywhere near what Norwich have offered."