The right-back, who has been playing at left-back at Euro 2024, is in danger of losing his place.
Fans have criticized boss Gareth Southgate for using Trippier as his left-back, along with Phil Foden as a left winger.
Speaking on BBC Radio 5 Live's Football Daily podcast, ex-striker Rooney said: “At the minute, it's Tripper or (Joe) Gomez, for me, who should play there.
“I was very surprised and really shocked that Ben Chilwell didn't get picked - just for the balance of having a left-footed player there.
“He plays at Chelsea and has played well for England in the past. He's a good left-back - he's been in tournaments as well - so I was really surprised he wasn't selected.”
Rooney was then asked: “So do you play Tripper or Gomez there? Do you bring Kyle Walker across?”
Rooney continued. “Over the past few years, Kyle has been the best right-back in the world. Do you take that away from him and put him at left-back? There's so many imbalances about the team.
“Should Foden play on the left, on the right, or as a 10? There are so many questions.”