The 19-year-old was hoping to be involved during the current campaign after featuring in the Gunners' pre-season before a serious knee injury in training ruled him out until his return to the reserves in April.
The Ghanaian-born player admits he endured a difficult period, at times fearing he may be left behind and even questioning whether he would ever return.
At the same time Frimpong watched from the sidelines as the Gunners lost the Carling Cup final and then tumbled out of contention in the Barclays Premier League, FA Cup and the Champions League.
Frimpong told the official club website: "Next season could be Arsenal's season and next season could hopefully be my season.
"I am quite confident if I don't get injured I can do something big.
"You have to stay injury free, sometimes it is just down to bad luck. Hopefully next season I'll have a good year and won't get injured."
While Arsenal visit Stoke City on Sunday, the match is followed by the clash between Manchester United and Chelsea.
Frimpong admits that although the Gunners have a small glimmer of hope, the title is likely to end up at either Old Trafford or Stamford Bridge.
WAITING AROUND
"There is hope but if you have to be honest you have to think either Manchester United or Chelsea are going to win it," he said.
"There is still hope, I'm sure the players aren't going to go on to the pitch and think they are just going to play for second or third, they are still going to fight to the end. That is what the manager has been saying.
"Most people did think Arsenal would win something this year but that's football, you can never rest on your laurels."
As for his own travails since August, Frimpong admits to having had self-doubts.
"At the start it was very tough because sometimes I thought I might not even come back and play again so hard when you see players going out and training, you don't know what to do with yourself.
"It was tough and hard to get over it."
He added: "When you've been injured for so long the club isn't going to be waiting around for you to get fit.
"They have to move on. That's where sometimes it was tough because people are looking to take over your place even though they are old friends.
"Everyone is here just for their own career so when you are back training you just have to put in your whole effort and see how things pan out."
source : www.arsenal.com