Sturridge has been impressed by Crystal Palace's highly-rated forward Zaha, who was a late addition to the squad.
He said: "He is a very talented player and he was sharp in training today, he looked very good. He has got a lot of skills and can bring a lot to the table. I am looking forward to playing with him."
The 20-year-old is also eligible for Ivory Coast and could still switch allegiance even if he plays in Wednesday's friendly.
Sturridge said: "I think whichever decision he makes is going to be right for him as a person but I think everybody would love him to play for England and it would be great if he could."