A graduate of Saints' academy, the full-back, who does not turn 19 until July 12, has already made 54 first-team appearances, attracting admiring glances from Chelsea and Manchester United.
Those performances have also caught the eye of Hodgson, who has indicated the England Under-21s international could feature in the senior team's friendly with Denmark on March 5 and soon be on the plane to Brazil.
The England boss has spoken privately with Saints manager Mauricio Pochettino about the development of Shaw and the club's other England players, with Perez confident in the teenager's ability to step-up to the national team.
"We don't know what Hodgson is thinking about in terms of the squad," said the Spaniard, who saw Rickie Lambert, Adam Lallana and Jay Rodriguez called up for England's last batch of games.
"We know he has followed our team often - he is at St Mary's or when we play away - so he knows perfectly our players.
"It is going to be great news if some of our players will go to Brazil, but the most important thing is now: let the players play and be relaxed. They are getting all they deserve.
"Luke Shaw is a quiet player with great quality and just with his job and his performances I think he will deserve everything. I don't know if it will be now or not, but his future is massive."
While Hodgson name-checked Saints' existing senior internationals, as well as England age-group players James Ward-Prowse, Nathaniel Clyne, Calum Chambers and Jack Cork, it is Shaw's name that is grabbing the headlines.
The left-back has been constantly linked with a move away from St Mary's and could soon have to deal with the additional pressure of being a senior England international.
Perez, though, is confident Shaw can cope with the spotlight, despite his tender years.
"Luke Shaw shows every day that he is a normal person, with great quality," the assistant said. "This is the best skill to be a top player.
"Obviously he needs time to improve, but he has no worries about the media talking about him or his chances to go to Brazil.
"His behaviour is normal daily. He just trains, enjoys it, talks with the lads the same age, so he is a normal player. This is the best way to improve and to achieve everything you want to achieve."
For Shaw and his Southampton team-mates, the immediate attention is on Saturday's FA Cup fifth-round tie at Sunderland. Gaston Ramirez and Dejan Lovren remain absent for the clash, despite making impressive progress from ankle ligament issues, in which Saints will look to make amends for their Capital One Cup exit to the Black Cats in November.
Gus Poyet's side have gone onto reach the final of the competition and also have a relegation dogfight to contend with, but Perez does not think that will necessarily help Saints' cause.
"Just before the press conference, we were talking about how Sunderland will prepare this week because yesterday their game at Manchester City was cancelled," he said.
"For all teams, the most important thing is to be focused on the next game because if you are winning you are getting confidence and improving your team.
"It is difficult to decide 'this game is better, don't play with the best team'.
"Obviously they are fighting to save their Premier League status and in a few weeks have a final, but the best medicine to give faith and keep the team fit is to try to win the game, so we expect a good team from Sunderland to try to beat us."