Speaking to Czech newspaper Sport, Rosicky said: "I think I will be back in the autumn.
"According to my fitness coach Tony Colbert I could have been playing at the end of the [last] season as he thought my fitness was okay. I think it was obvious from the training that I was ready to play, if not for 90 minutes.
"But the club decided not to play me. They saw that I was okay, but maybe they just did not want to take the gamble.
"Until I play in a league match I will not be able to tell what my chances are, but when it comes to fitness alone I am in better shape than when I came to Arsenal."
The Czech midfielder added: "I am missing the competition. Playing alongside Cesc Fabregas and Theo Walcott makes you feel comfortable and I think that I will quickly forget that I have been out for a while.
"Now that I have recovered, I am a new option for the manager.
"We have a strong team capable of moving mountains in all competitions."