As reported, Iraola, who left Bournemouth having guided them to a first European qualification at the end of the season, is the frontrunner for the job at Anfield.
Liverpool, according to the Times, are keen to make a swift appointment after they sacked Slot on Saturday, and want to have his successor in place by the start of the World Cup.
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Iraola has had discussions with other clubs including Crystal Palace, Bayer Leverkusen and AC Milan over vacant positions, but, while the Reds will consider others for their head coach role, the Times indicates it would be a surprise should he not be appointed.
The Daily Mail, meanwhile, has reported that Iraola is keen to take the job.
A move to Merseyside would bring a reunion with Richard Hughes, who brought Iraola to Bournemouth as club technical director, before he moved onto Liverpool.
Hughes has reportedly been charged with turning Liverpool’s fortunes around after a disappointing second season with Slot, where the club finished in fifth.
They want to return to a more aggressive style of football which Iraola would bring. The Basque boss would also join up with former Bournemouth left back Milos Kerkez, who joined the Reds last summer.