The 20-year-old has made just a substitute appearance for the Gunners in their League Cup tie against Coventry City in September since recovering from a knee injury that kept him on the sidelines for nine months.
"I still don't believe I am 100% right - obviously I am playing but I don't think I am ready for the first team yet," Frimpong told Arsenal's official website. "I still need two more 90-minute games [for the Under-21s], then I will be fine.
"It is difficult when you play for the Under-21s, because even though you're playing for points it is still not as competitive as a first-team game. The pressure is totally different.
"But coming back from a nine-month injury, I just have to make sure that when I come back into the team, I am right and ready. I don't want to push myself if I am not ready.
"Once you keep playing you build up your confidence and everything falls back into place. But I am sure that when the time is right and I am called upon, I will do a good job for the team."
Frimpong suffered the injury while on loan at Wolverhampton Wanderers last season.