Oxlade-Chamberlain sealed his transfer to the Reds on deadline day and is seeking a new challenge in his career.
The England international is hoping to establish himself in midfield at Liverpool, but as he learned first hand at Anfield on Sunday, breaking into the team will not be easy.
Keown believes that Holland international Wijnaldum is most vulnerable to his arrival.
He said: "I don’t think he has really fulfilled his potential at Arsenal... and if he thinks central midfield is his best position then he has some work to do.
"I do think he could be one of the midfield three at Liverpool, where he could play instead of Georginio Wijnaldum."
Wijnaldum arrived with similar doubters last summer after a mixed season at Newcastle, but he went on to prove himself a worthy part of Jurgen Klopp's team.
He scored the crucial goal on the last day of the season last year which eased their path into the Champions League, and perhaps convinced Oxlade-Chamberlain that Liverpool is the better club for him to be at rather than Arsenal.
Wijnaldum has started all three games in the Premier League this season, and as Keown points out, he may well have a new challenge on his hands.