Frimpong, 21, made his debut for Fulham in Saturday's goalless draw at Norwich, having moved across London for the second time this season after a short spell at Charlton.
The tough-tackling Ghana-born midfielder, who came to London aged eight, has battled back from two serious knee injuries which have hampered his progress.
Wilshere has been through his own fitness battles, recovering from more than a year out to return in great form for the Gunners and produced a man-of-the-match display against Brazil at Wembley last week.
Frimpong came through the Arsenal youth system alongside Wilshere, and has his sights set on a similarly bright future.
"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," Frimpong said.
"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."
Frimpong added: "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," the midfielder said.
"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."
Frimpong represented England at youth level, but in November 2012 was cleared by FIFA to play for Ghana.
Although he missed out on the African Nations Cup squad, Frimpong hopes it will not be long before he lines up for the Black Stars.
He added: "The [Ghana] manager said to me 'make sure you do well for your club side and after the African Nations Cup, I am going to call you up."