Parry said: "We did not want any of the muddying of the waters or the indignity of clandestine talks taking place while Gerard was still around, so we start now. One of the advantages of spending a few days away is that I get a clear head and perhaps a bit of time away from the phone to think it through. The criterion has to be who is most likely to help us become a challenger."
Rather surprisingly, given the intense speculation linking the club with Valencia coach Rafael Benitez, Parry has made it clear that he has yet to approach any manager concerning the managerial post.
"Not at all. It is one step at a time and the process starts now," said Parry.
The Anfield Chief Executive has laughed off many newspaper reports since the axe fell on Houllier on Monday, but he concedes talk of meetings with Curbishley are the 'most bizarre' yet.
Parry added: "That is probably the most bizarre story of the week, and there have been some pretty bizarre ones. I don't think I saw Alan Curbishley at all that day, apart from looking down at him on the touchline with some dismay."