The England international moved to Liverpool FC in a £40m deal from their title rivals Arsenal on transfer deadline in the summer transfer window.
Oxlade-Chamberlain had the option to move to defending Premier League champions Chelsea after he passed a medical at the west London club.
Arsenal offered the versatile midfielder a new contract but Oxlade-Chamberlain was purported to have opted to move to Liverpool FC in order to secure a central midfield spot.
Liverpool FC boss Jurgen Klopp made Oxlade-Chamberlain wait for his first start in the Liverpool FC team before he scored in a 7-0 win over Maribor in the Champions League.
The England star netted on his Premier League debut in a 4-1 win against West Ham United at the London Stadium at the end of October.
Oxlade-Chamberlain has now started seven games in all competition over the past two months to start to leave his mark at the Anfield outfit.
However, Arsenal boss Wenger has warned Oxlade-Chamberlain that he still isn’t guaranteed a starting spot at the 18-time English champions.
“Is he sure of a place there? You are sure of a place nowhere,” said Wenger at a news conference last week.
“In a big club, you have big competition with some good players. That is absolutely normal. What do you want to be, a big player and not have to fight?
“You can’t be a big player, sit in your rocking chair and say, ‘I do not want to fight’. It doesn’t work like that. Every player has to fight.”
Oxlade-Chamberlain won three FA Cup in four seasons at the north London outfit.
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