The Scot, who was recently named as a non-executive member of the Reds' board believes that the German international has given the Gunners the added quality to maintain a push for the title.
"The way everybody is praising him now, it looks like [manager] Arsene Wenger has wiped the slate clean with the signing of Mesut Ozil," Dalglish wrote in his column in The Mirror.
"With the football education he has had, he will not be one to shirk his responsibilities when it comes to tracking back either.
"His arrival seems to have changed everything, but we'll find out how good the Gunners really are in a few weeks' time. The rest are going to have to work hard to knock them off their perch."
Wenger's side travel to West Bromwich Albion this afternoon.