The winger has been linked with a move away in recent weeks.
The winger has once again failed to impress this season, with a series of disappointing performances when handed his chance in the first team.
It has so far been a disappointing time in London for him, after being hotly tipped to be a big star in future when breaking through at Southampton.
In fact, there is now talk that he could leave the club in the near future, but Redknapp has told him to prove himself at the Emirates before thinking of a transfer elsewhere.
“Alex Oxlade-Chamberlain has achieved nothing at Arsenal yet, so why would he want to leave?” he told the London Evening Standard.
“He hasn’t achieved what we expected of him in his career so far. I hear Arsene Wenger keep saying Oxlade-Chamberlain can play centrally, but he needs to do it consistently in whatever position at the very highest level.”
“Now is the time to kick on and repay the faith Arsene and his staff have shown in him. He needs to establish himself at Arsenal first before thinking about going anywhere else.”
The problem for Oxlade-Chamberlain is breaking into an Arsenal midfield that is already jam packed with talent.
A central position seems out of the question, with Mesut Ozil first choice in the number ten role and the likes of Santi Cazorla and Aaron Ramsey also impressing in central midfield.
On the right wing there is equal competition, with Ramsey again a competitor and Joel Campbell having stepped up and proven his worth this season.