The Reds sacked Arne Slot on Saturday, just a year after the Dutchman guided them to the Premier League title.
The club hope to have a successor in place as soon as possible, with departing Bournemouth manager Iraola the leading contender.
The 43-year-old delivered the Cherries' finest season to date with a sixth-placed finish - only one spot and three points behind Liverpool in the table - to qualify for next season's Europa League.
Full story: BBC Sport
