Mark Hughes resigned as manager of Fulham on Thursday and immediately brushed off speculation linking him with the vacancy at Premier League rivals Aston Villa.
Fulham finished eighth, one place above Villa, last season and Hughes was immediately touted as the man to replace Houllier.
However the former Manchester United, Barcelona and Wales striker said in a statement: "I hope the supporters and all those connected with the club will understand I wish to move on to further my experiences.
"I would also like to take this opportunity to clarify that neither myself nor my representative have approached or have been approached by another club."
"This decision to leave Fulham has not been influenced by any outside party," added Hughes, who began his managerial career with Wales before spells with Premier League sides Blackburn Rovers and Manchester City.
However, it would be astonishing if Hughes had quit Fulham with absolutely no plans of any kind for another job.
The 47-year-old enjoyed a successful first season at Fulham that also saw the London club earn a return to Europe via the Fair Play League and was understood to have a good relationship with chairman Mohamed Al Fayed.
He said: "I would like to thank the chairman, directors, players and fans of Fulham Football Club for their support over the last 12 months and wish them every success in the future.
"I believe my management team and I have done a good job and the club has a strong foundation from which they can go forward.
"I have especially enjoyed our excellent relationship with the chairman and chief executive (Alastair Mackintosh).
"I sincerely wish Fulham a successful campaign in the Europa League next season and for their continued progress on and off the field."
A brief Fulham statement said: "Fulham Football Club can confirm that Mark Hughes has provided notice, under the terms of his contract, to leave the club at the end of June.
"After discussions with Mark the club has agreed to accept this notice."
Source: AFP Global Edition