Liverpool chief executive Rick Parry has revealed the club would be looking for a new manager ''with a proven track record''.
He said ''quality would be the watchword'' be it a British or foreign coach to replace Gerard Houllier.
The Frenchman's six-season reign has come to an end even though Liverpool secured a fourth place finish to ensure Champions League qualification.
Now the search begins for a successor to Houllier, who took over sole responsibility in July 1998.
Parry said: ''It is about raising the standards still further and getting us back to being a contender.
''The question is: 'Who is the candidate who is most likely to help us challenge for the title?'
''That is easily said but a bit more difficult to identify and the thing we are going to bear absolutely uppermost in our minds.
''Track record is obviously going to be important. If you are looking at someone's ability to win trophies, there is some proof they have done it. That clearly helps.
''It won't be the only criteria. Commitment, enthusiasm, hunger will be very important too.
''I don't think we are going to have a dogmatic British versus foreign attitude. It is going to be quality will be the watchword.''
Houllier wanted to carry on but in the end bowed to the board's wishes with club stating ''they had parted company''.
''I want to make clear how much the club means to me. I had intended to carry on my job,'' said Houllier, who wants to continue in football.
''But the reason we have agreed to part company is mainly because of the sudden excessive pressure on the board and myself.
''The pressure is something I can cope with, though some of you have tested me over the last ten months.
''But I thought it could be harmful for the players in next season's campaign and I also thought that it could jeopardise their performance and achievement.
''That's why we have agreed to come to this situation.''
Houllier said he would retain a lifetime affection for Liverpool.
''The club comes first, I'm not here for myself, I'm here for the club. The club will always come first for me.
''I arrived here six years ago as a Liverpool supporter and I leave as an even bigger supporter.''
Parry said: ''It is the right time to be making the decision frankly. You have the close season to get it right. It is urgent to get it right. It is terribly important we get the right candidate. If it takes time, then that will be time well spent.''
Parry said that Houllier had become a victim of his own success.
''Gerard raised the bar and set the high standards. The last two seasons have seen us dip.
''Clearly we fell short. Yes the minimum requirement was to finish fourth but that is not the aim.
''The aim for Liverpool is to be challenging. It was clear early on we weren't.
''You couldn't possibly say it was a great season. In the final analysis we kept the debate very simple, it was all about to making sure we are a contender.
''The debate focused on a single issue. Did we feel we were going to be a contender for the title next season without making a change.
''Everything really turned on that. For a variety of reasons we felt that without a change, we couldn't necessarily see things improving dramatically.
''A change was needed to give us a kick start. But he has left us with very solid foundation for anyone coming in.
''He changed things off the pitch too, bringing back both our pride and self respect and instilling discipline and professionalism throughout the club.''
Alan Curbishley, Martin O'Neill, Rafael Benitez and Gordon Strachan have been linked with the vacant post.
Former Liverpool star Craig Johnston praised Houllier for the ''outstanding'' job he did at Anfield.
''The happiest thing is that his departure seems to have been done in an amicable way with the dignity he deserves,'' said the Australian.
''He has done so much for the club and embraced what it's all about. Whoever they get, they will not get a man as caring and passionate with the understanding of what it takes to make Liverpool great.''
Former Liverpool striker David Fairclough sympathised with Houllier but felt the club were right to seek a move in a different direction.
Fairclough said: ''It was the right time to consider what had gone before and look at last season.
''He had one more year on his contract but realised the pressure was building and it would be very difficult to continue.
''It is probably the right time. A great deal of fans had lost faith and there were questions over who he would buy in the summer.''
Ray Houghton, who was a member of the last Liverpool side to win the title in 1990, believes Martin O'Neill would be an ideal replacement: ''He's a man who sticks out straight away. He's done an excellent job wherever he's been. He has a fantastic record and I think the fans would take to him.''
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