The Dundee United boss, who also works with Levein in the Scotland set-up, believes that the Scottish Football Association should have already reached its decision.
Houston told BBC Sport: "If the SFA decide that they want to remove Craig, it shouldn't take three weeks or so to remove him.
"Fair enough, the SFA were wanting to let the whole situation calm down a bit before discussing that but now they have discussed it over two days, and I am going with what I am reading and hearing, it shouldn't be that hard to make that decision.
"That is not my business as such but I still regard Craig Levein as one of the top managers in the game, I have worked with him so long, I know how good he is and I would like him to get that opportunity to stay on."
Levein's position has been called into question as Scotland are bottom of their World Cup qualifying group after four games.
A decision on Levein's future is expected this week.