Tottenham boss states veteran midfielders Steven Gerrard and Frank Lampard should also go to the tournament in Ukraine and Poland as their quality and experience is invaluable
Redknapp is the favourite to replace the Italian, following his resignation last week, and stated if he was the Three Lions boss he would pick the veteran playmaker for the tournament in Poland and Ukraine.
He told reporters: "Let's be honest, you would love to have Paul Scholes in the Euros this year," he said. "He'd be in your team, he's that good.
"Whoever's there would love to take him, I'm sure. You'd love him to play. He plays like the Spaniards, like Xavi [Hernandez] or [Andres] Iniesta. He does not give the ball away."
Despite their advancing years, Redknapp also stated Frank Lampard and Steven Gerrard should definitely be in the England squad, as he believes their experience and quality is essential to the team.
"You need men in your side, you need characters if you are going to win anything," Redknapp continued.
"Frank is still a top player. You write Frank off at your peril. He's still a top player in my opinion. Stevie Gerrard is still a top-class player. We have got some good players in our midfield."
The 64-year-old also believes Gerrard is the outstanding candidate to take over from John Terry as England captain but feels his own player at Spurs, Scott Parker, could lead his country.
He added:"I think there are some good candidates. Gerrard is a good candidate. Stevie Gerrard is a fantastic player. There are one or two who could do it. Scottie could do it, for sure, but so could Steve."