The 18-year-old left-back has enjoyed a breakthrough season with Saints in the Premier League and is being strongly tipped to secure a plane ticket to Brazil this summer.
Shaw, who was a reported target for a number of Premier League clubs in January, is set to make his international debut in March when England host Denmark in an international friendly at Wembley.
With Ashely Cole and Leighton Baines also in contention, Shaw faces a fierce battle to feature but Perez believes the teenager is improving every day.
"When you see Luke daily you can realise the top quality he has," he told the Daily Mirror.
"We see Luke just moving on and on, he is aware of the situation with people talking about him but it doesn't affect him.
"He is a normal person and everyone loves him."
Shaw has featured in all-but three of Southampton's top flight matches this term and Mauricio Pochettino's right-hand man expects Shaw can emulate Saints team-mates Ricky Lambert, Jay Rodriquez and Adam Lallana in gaining full international honours.
"I don't know if it will be now or not, but his future is massive," Perez added.
"He is doing well like our other England players and hopefully as many as possible will play in Brazil."