Liverpool will announce their new coach within the next two weeks, chief executive Rick Parry said on Monday.
Parry said on Sunday a manager would be in place by the end of June, but has brought that forward by a fortnight.
That could mean negotiations have begun with either Valencia's Rafael Benitez or Charlton's Alan Curbishley.
"There will be an announcement about our new manager in two weeks," said Parry. "Further to that I do not wish to comment on speculation."
Benitez, who led Valencia to the Spanish title and the Uefa Cup this season, is favourite to replace Gerard Houllier, who was sacked earlier this month.
But Valencia are fighting to keep their manager, and have offered him a new contract.
Curbishley, who has been in charge at Charlton since 1991, has also been tipped to move to Liverpool.
But Jose Mourinho, who has confirmed he is leaving Porto for an unnamed English club, is likely to choose Chelsea ahead of Anfield.