Barry and Parker are back in camp preparing for the September 23 title defence against Fury in Manchester.
It will be Parker's debut in the United Kingdom which has now supplanted the United States as the hotbed of the heavyweight scene.
Parker is eager to make an impact, knowing an impressive win over Fury will be a huge step towards bigger fights and bigger money.
"We are really excited about having our first fight in the UK. We have been trying to get there for the last 18 months. We need to explode on the scene in the UK," Barry told Boxing Scene.