Manchester United manager Louis van Gaal named Rooney as the Red Devils' new skipper on Tuesday evening, and there is a vacancy for the Three Lions following the international retirement of Steven Gerrard earlier this summer.
Blues centre-back Jagielka, who plays alongside Rooney for Roy Hodgson's side has backed his international colleague to be handed the captaincy by the England manager.
He told ITV Sport: "If you look at the way he's matured over the last few years, obviously there's games where he probably does get a little too heated up, but that's what we love about the way he plays – his passion.
"And I'm sure the England fans would love that as well. I think it's definitely a good decision for Manchester United to make him captain and I think the way he's progressed over the last few years, settling down with a family and all sorts, I think he'd be a great choice as England captain."
Everton begin their new Premier League season with a trip to Leicester City on Saturday.