Rosicky has been thrilled with Gnabry's contribution and anticipates further progress under boss Arsene Wenger.
"He has a manager here who will develop him and who has a history of developing young players," Rosicky told arsenal.com.
"Nothing better could happen to him than being offered a new contract here.
"He is a good dribbler and can take on you on in the one-on-one situations. That can be his strong point in the future and for an 18-year-old he is doing very well.
"He is a very talented boy, 18 years old and he still has plenty of things to learn and he will find no better place to learn than here. I think it works very well for both sides that he stays here.
"He's got a great environment for his growth and the potential and talent is there, so let's see how he will develop."
For the big stories and the banter follow us on Twitter: @tribalfootball