BBC Sport understands Elphick, a lifelong Liverpool fan, has had no contact yet from the Reds but would be interested in the opportunity.
The former Bournemouth centre-back, 38, turned down the opportunity to become the Bristol City manager last week in order to assess his other options.
The hiring process at Anfield is being led by Richard Hughes, Liverpool‘s sporting director, who previously worked with Iraola at the Cherries.
The Reds sacked Slot on Saturday, just a year after the Dutchman guided them to the Premier League title.
