"Whoever it is doesn't have to have played alongside me at Arsenal - a young Jose Mourinho would do me fine.
"There are a lot of considerations when it comes to compiling a backroom staff. We have a lot of French players here so maybe the French route is an option."
Keown retired three years ago and helps out with coaching at Arsenal.
He played alongside Adams in the Gunners' central defence from 1984 to 1986 and again from 1993 to 2002, when Adams retired, helping them to the league and FA Cup Double in 1998 and 2002.
Keown, who collected 43 England caps, also won another Premier League title with Arsenal in 2004 before spells with Leicester and Reading.
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