Aubameyang's deal with the Gunners runs out next summer but he is yet to agree to an extension and is linked with a move away from the Emirates Stadium.
Keown told talkSPORT: “I think the message needs to be to the player 'look, we can't have you captaining the club if there's uncertainty around your contract', in the last year of his contract, that can't be allowed to happen."
“I think he'll leave with a heavy heart," the former England defender added.
“I think he's the nearest thing I have seen to Thierry Henry at the football club and the club will have to make swift decisions.
"They can't allow what happened a few years ago with the transfers just going on and on. The club needs direction."