However, Willian impressed against Leicester City with two assists in a 3-1 victory on Sunday afternoon, but Keown believes that the 32-year-old has looked "glum" since his free transfer last summer.
Speaking to BT Sport, Keown said: "Well, I saw in the week about him saying he wanted to stay at Chelsea. Is he a player almost in mourning because he's missing Chelsea?
"He's now an Arsenal player, he's got to give his best for the football club, they've rewarded him with a three-year contract but he hasn't really performed.
"It's almost not being in the mood, he's looked glum as a player so he's got to play his way in now. There's been some minutes on the pitch, let's see what he can do. He's always been a player I admired at Chelsea but I've not seen the same in an Arsenal shirt."
Willian has provided five assists in all competitions this season, but he has now gone 27 matches without opening his goalscoring account for the Gunners.