The 18-year-old winger joined the Gunners from Southampton at the beginning of August for a fee of £12 million, which could rise to £15 million with add-ons.
Oxlade-Chamberlain believes that he can mirror the form he showed at Southampton in the Premier League with Arsenal as a major part of Arsene Wenger’s starting line-up.
He told Sky Sports: "He's [Arsene Wenger] just told me I need to put pressure on him, impress him in training and that's all I can do.
"He's just bought some new players now and I understand it's going to be hard for me, but I'm a young lad coming into the club and I understand I've got a lot of hard work to do to try and impress him."
The youngster also said admitted he was worried he would be intimated by the stars at Emirates Stadium, but is confident that he feels at home at the club.
"I've settled in well. At first I was a little apprehensive going in maybe, but all the boys have welcomed me nicely and I'm getting into the swing of things.
"I understand there is a lot of hard work to establish myself and get in amongst it, but it's going well for me."
The England Under-21 international has also lavished praise upon Wenger’s other signings, which were made towards the end of the transfer window – Per Mertesacker being the standout addition.
"I don't think Arsenal would buy anybody who isn't a good player," he added.
“I've seen the likes of Per Mertesacker play and they look like quality signings. I think they will do a good job for us and help us to do well this year."
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