He has also backed fellow defender John Stones as a possible replacement in future.
Jagielka is the current holder after the armband having replaced Phil Neville in 2013 following his departure.
At 33 he arguably has several seasons let in the tank for the Blues first team, but talk has already begun about who could replace him in the role.
John Stones has been touted as one option, as well as a future England captain, while some believe that the armband should go to midfield star Ross Barkley.
Jagielka though, says he believes that full back Coleman has all the qualities necessary to take up the mantle.
“We’ve got a couple of leaders and Seamus Coleman is quite vocal,” he said in an interview with JD Football.
“His mannerisms on and off the pitch are fantastic. People talk about John as well because of his position and natural coolness, so it would be between them two.”
“But at the top of that at the moment would be Seamus with his extra little bit of experience and the extra use of his voice.”
Who ends up as Everton captain between Coleman and Stones is likely to depend on whether both are still at the club in the future.
Stones in particular looks like one that could depart Goodison Park, with a number of Europe’s top sides all having been credited with a firm interest in securing him at some point.
The Blues are naturally keen to keep him though, and should he stay, it seems there will be a fierce fight for the captain’s armband when Jagielka eventually steps down.