The Ghana midfielder, on loan at Fulham for the rest of the season, made his debut for the Cottagers in the goalless draw at Norwich.
Frimpong, who came to London from Ghana aged eight, has battled back from two serious knee injuries which have hampered his progress in north London and has kept a watching brief on Wilshere since the England midfielder's return.
The 21-year-old, came through the Arsenal youth system alongside Wilshere and said: "That is football, sometimes you are going to get good luck, sometimes you are going to get bad luck, and I have had loads of injuries, but I mean to get over it just like Jack has.
"He has got over his injury and now he is playing for England. That is what I trying and do - to get over my injuries and start playing football on a regular basis."
"Jack is a great footballer. For his age and for what he is doing, he is an inspiration obviously because every young player in the Premier League wants to achieve what he is doing.
"Since I have been here, I haven't really spoken to him, but when I am at Arsenal, we do speak on a regular basis. I am happy for him and what he is achieving in football."
Frimpong hopes he can gain a regular run in the Fulham side to return to Arsenal ready to impress next season.
"The boss at Arsenal, Mr Wenger, told me to come here and get some games because there is no point sitting on the bench at Arsenal," he added.
"He said to come here and show what you can do, get some games under your belt, then come back next season and see what happens."