The 28-year-old arrived at Everton from Spartak Moscow in January short of fitness due to the winter break of the Russian league.
McGeady made five starts and 13 substitute appearances and has set his sights on being in manager Roberto Martinez's starting line-up on the opening day of the next campaign.
"I haven't played all that much at the club so far but I'm just looking to play as many games as I can before the end of the season and hopefully have a good summer, keep myself in good shape and come back to hit the ground running in pre-season," McGeady said.
"It's getting into that rhythm of playing 90 minutes every week and getting up to the tempo of the Premier League.
"Hopefully that's what I'll do next season. The aim for me is to be in the starting XI in the first game. I spoke to the manager before we left and I said I wanted to carry on through the summer.
"I had a break at Christmas and he said I still need to give myself a rest from playing and running for a couple of weeks."
Meanwhile, Martinez is working on his plans to strengthen his squad for the next season, with Everton having a Europa League campaign to contend with.
"Recruitment is vital. The recruitment department have been working tirelessly to get the reports and highlight the targets and players that are going to fit in our football club," Martinez said.
"We've identified the players and now it's about making sure we can get them to join. It's very much an important period, but it's not one where we need to panic.
"We don't have to make decisions just to bring numbers into the club. Everything has to be measured and everything needs to be taken on the understanding that bringing the wrong player into this special group of players that we have could have a very negative effect.
"It's a key period to make the right calls and the right adjustments, but recruitment is going to be vitally important because of the demands of European football. It's something we want to embrace.
"We don't want to feel that we have to blame European football as the reason we cannot keep the standards in our domestic league."