Williams told the Ilford Recorder: "We will be making some phone calls, but I can't see anything happening before the weekend.
"We will be out all week looking, but it's a case of getting the right person in within the budget."
Unlike when Sir Alex Ferguson left Manchester United, a new Arsenal head coach will not be under immediate pressure to land a premiership title.
The latest gossip and rumours from the newspapers and online: The Daily Mail reports that Lemar's Monaco team-mate FABINHO is
Gianfranco Zola's troubled reign as Birmingham manager continued with defeat to QPR on Saturday, meaning he has taken just six
The latest gossip and rumours from the newspapers and online:Liverpool manager JURGEN KLOPP is in line to be Barcelona's next
The latest gossip and rumours from the newspapers and online:ARSENE WENGER will end his long reign as Arsenal manager in
Arsene Wenger's position as Arsenal manager has come under increased scrutiny following Wednesday's Champions League thrashing at Bayern Munich.