The defender has had a breakout season at the Foxes this campaign and Gareth Southgate has increasingly used him as England's first choice left-back since the World Cup.
Man City are thought to be keeping faith in Benjamin Mendy, for now, but the 22-year-old remains a player admired by the Eastlands club. Chilwell also continues to be linked with the likes of Tottenham and Napoli.
Bridge, who played 58 times for City, thinks that the left-back would thrive under Guardiola.
"He is very good and he has shown that at Leicester," Bridge told Goal. "I think if he does make that move then it will make him a better player, but I also feel if they do get him in and they do want him, that Pep will want to improve him and make him that player that fits them.
"It will make him a better player and then I think he could become England's undisputed best left-back."
Leicester's season looks to be petering out, as they remain outsiders to qualify for next season's
Chilwell will also play in the Nations League semi-final at the end of the season, with England chasing their first piece of silverware since they won the World Cup in 1966.
"He broke his leg and has had a tough time at United, but he has come on a long way since his injury," Bridge said of Shaw. "To come back from that, all credit to him. I have to mention Ryan Bertrand who I still think is a talented player and deserves to be in the mix.
"I think Luke Shaw is England's best though. What I expected is that he would move on and get better at United, it has taken him time, but I still think he is a better player overall than other left-backs in this country. He is quick, strong and intelligent.
"He has progressed of late for Man United and he is one of their better players. He should be Gareth's first choice left-back."
Wayne Bridge was speaking at the London leg of The Official Coca-Cola Premier League Trophy Tour. Find out more about the tour at https://www.coca-cola.co.uk/trophy-tour #TheOfficialTrophyTour