The 18-year-old winger joined Arsenal from Southampton for an initial £12million in August.
But Pulis admits the teenager was high on his list of summer transfer targets.
“We were well aware of the situation, but when you’ve got Manchester United, Arsenal and the likes chasing him, you understand where you are,” said Pulis.
“The kid is a future England star and I think he could even go to Euro 2012 if he plays enough games, he’s that good,” added Pulis.