The Toffees look ahead to their last four fixtures of the campaign and are eight points off Totttenham in fifth.
Rodwell believes that his in-form side can cause an upset by qualifying for the Europa League and is focused on pushing forward in order to end the season on a high.
He told skysports.com: "We have hit form. We started off badly but we are climbing the table now, so that's good.
"We always seem to do that recently, start off slowly and then leave it late to try and get as high up as we can. But there are still quite a few games left, so hopefully we can do it.
"It is an outside chance, but we have really found some form now so we will just concentrate on keeping that up and doing as well as we can in each game."
The Toffees currently sit one place below rivals Liverpool with five points separating the two sides, and the 20-year-old midfielder is targeting a first finish above their neighbours since 2005.
Rodwell said: "For the fans, that's another thing we want to achieve. We are sneaking up behind them, so hopefully that's possible as well."
After losing a number of key attacking players to injuries, including Tim Cahill, Mikel Arteta and Marouane Fellaini, Rodwell was full of praise for striker Jermaine Beckford, who has been drafted into the side of late.
He said: "We have had a lot of injuries this season, recently with the likes of Fellaini and Saha, who has been a big loss to us. But Becks has come in and done really well so I think we have a good enough squad to cope."
Injuries to the side have also seen Everton boss David Moyes forced to call upon players from the Toffees’ youth team, something which Rodwell can relate to as he rised through the clubs ranks himself.
Rodwell praised the system, which nurtured him into a Premier League regular and potential future England international, and offered his academy successors advice.
He continued: "The bench the other day, virtually every one was an academy player. It's good for the young lads and they will get their chance.
"You just need the confidence and you need the experience, so hopefully they will get that and they will make the step up like I did.
"The academy system is really good and it just seems to keep on getting stronger. Hopefully there will be a few more come through this season and next season and challenge, with a few knocking on the door already."