Sweden international Olsson has just over 12 months remaining on his current deal with the Baggies and had originally wanted to wait until after Euro 2012 before making a decision.
Olsson said: "I want to hold off definitely until I know who is going to be in charge. That's what I've been saying to Dan Ashworth (Albion sporting and technical director).
"It's important to know who is going to manage the club and I think that's a fair request before you speak about your future. That's where we are at the moment.
"Since New Year I have spoken regularly to Dan and, before the gaffer got the England job, it was very uncertain about his future here and that was my reason then for not speaking further.
"I wanted to know who was going to manage the club - and that is even more relevant now with the gaffer taking the England job."