The Toffees left-back says that, given his experience, know-how and talent, the centre-back and current deputy captain is the natural successor to Phil Neville
The 28-year-old full-back says his team-mate Jagielka is the logical choice for the armband, having provided suitable and apt cover for Neville over the last few seasons.
"He is ready now to step into that role. It is a loss to lose Phil [Neville], but it has worked well because Jags [Phil Jagielka] has been doing it for a little bit and has had a chance to bed into that role in that time." Baines told the club's official website.
Baines gave his mark of approval to the proposed promotion, describing his Everton team-mate as a consumate professional and natural leader.
"He is one of the more dominant characters in the squad. He is very experienced now and someone that everybody can look to. It would be great for him, as he is quite vocal, as vocal as Phil was really, and he does lead by example as well," the England international continued.
The pair were integral to Everton's performances this season, despite Jagielka battling a number of injuries throughout. In the latter half of the season they conceded just 17 goals in 19 games - a record in the clubs history.
He added: "He had an amazing season. He wins every tackle, the blocks he makes - he is brilliant for us. If there is a better centre-half at the moment I would like to see him."
Picking the next captain is one of the first tasks awaiting new Goodison Park boss Roberto Martinez.