Gallagher is on loan at Palace from Chelsea for the season, and has played 26 league games this term.
"He is a player who brings a lot of energy, but he also has a lot of quality to go alongside that," Rooney said.
"I think he deserves his England call-up and deserves to play in those games, and I think he can play a big part for England going forward.
"He can be a player, like Declan Rice, that can be that engine of that England team. I would take him to the World Cup, he is a player who is appreciated a lot more by his team-mates and that shows signs that you are a good player."