The big Brit has started a 10-week training camp ahead of his November 26 IBF title defence in Manchester.
Joshua's promoter Eddie Hearn is set to reveal the opponent on September 26.
Bulgarian Kubrat Pulev and Canada's Bermane Stiverne are the favoured options though Parker, because of his mandatory challenger's position, is also in the frame.
Hearn has indicated he would prefer to have Parker fight David Price on the undercard as a way of introducing the Kiwi to the British market and building hype towards a showdown with Joshua in London in March.