The former defender can't Arsene Wenger allowing either player to leave.
There have been rumours that both players could be set to depart the club in the summer in recent weeks.
Oxlade-Chamberlain in particular looks like one who could leave having once again failed to impress when given an opportunity in the first team.
His poor form in particular has been emphasised by the likes of Joel Campbell coming into the side an impressing when given a chance.
Keown though, says that he can’t see either player leaving as Arsene Wenger won’t want to make radical changes to his squad.
“The basis of Arsene Wenger’s management has always been loyalty,” he told the Daily Mail.
“He is loyal to his staff and is loyal to his players. He’s very solid and stable in everything he does.”
“There are rumours of people like Alex Oxlade-Chamberlain and Theo Walcott departing but I don’t think Wenger will allow those players to leave. He won’t want to make radical changes.”
While Keown may not see Wenger wanting to sell either of those players, Oxlade-Chamberlain may have to force a move.
He has largely failed to realise his potential since breaking through at Southampton, but much of that has been down to injuries and a lack of game time.
A move elsewhere could see that change, and him finally becoming the star many predicted he would become when he was a young star for the Saints.