Fusitua admits to not having a lot of football knowledge, but got some help with introductions from renowned Liverpool fan Greg Eastwood.
"I don't follow football too much but I got a tip from one of the boys that the captain was there and his name was Jordan Henderson," said Fusitua. "I got a photo with him, that's one to keep. "
It was a galaxy of stars. Henderson, who also plays for England, is valued at about GBP 23 million ($40 million) on the open market. Coutinho could fetch double that while Sturridge is rated one of the best strikers in the English Premier League.
"It was pretty surreal," said New Zealand back rower Manu M'au. "All the boys were talking about those players [and] I was just sitting there looking at them, I couldn't believe it. I wanted to take some photos but I was just too shy."
Melwood, which was built in the 1960s during the reign of Bill Shankly, is a remarkable facility. It features three full size football grounds, including one that is made to the exact dimensions of Liverpool's Anfield ground (101m x 68m).
The pitches also feature full under soil heating, to combat the harsh winter months in the north of England.
Melwood also boasts rehabilitation rooms, a gym, a swimming pool, a press meeting room and a restaurant.
"They were top notch facilities and the grounds were fantastic," said Fusitua. "It was quite amazing.
The Kiwis completed another intense training session today - closed to all media and public - in the afternoon wind and rain.
The team have a day off tomorrow, before the captain's run at Anfield on Saturday (Sunday NZT) ahead of the game on Sunday (Monday NZT).
Autex - Proud sponsors of New Zealand rugby league since 1981.