The defender believes the Toffees can win a Champions League place and says they are looking to emulate the likes of Tottenham who have broken into the elite recently
The Toffees have only lost twice so far this season but have drawn seven of their last nine games in the Premier League.
Everton are notorious for their weak starts to the season before coming good in the second half but after their impressive beginning this campaign, they currently sit in sixth position, three points off fourth spot.
"It is going to be quite wide open," Jagielka told The Sun. "The last few seasons, the Premier League has gone a little bit crazy, with teams finishing almost anywhere.
"The title has been between two or three teams but the Champions League is there for anyone. Tottenham have done it, Newcastle had a crack at it [last season, before finishing in the Europa League].
"We have only got to look back at the last two seasons to see how we have started. We haven't given ourselves a chance.
"We aren't favourites to finish fourth by any stretch of the imagination but at least we are in the mix. It's no good if you are having to claw back a 20-point gap at Christmas."
Jagielka’s manager David Moyes has questioned whether his team have the consistency to mount a challenge, especially with injuries to key players and an already threadbare squad, and while Jagielka admits they have a small squad, he said it is not a concern for him.
"Whether we are underestimated or not, we have still not got a very big squad," he added. "We don't have that many options on the bench.
"Maybe that is why people are not talking us up. But it doesn't bother us. The squad isn't going to get much bigger, so it will be all down to how the manager manages us."