Slot previously retained the support of Liverpool's hierarchy at the end of April, and was even confident he would remain in charge next season when asked about his future last week.
However, after Chelsea captured Xabi Alonso, one of their candidates to eventually take over at Anfield, the Merseyside giants could pull the trigger on the Dutchman following a disappointing campaign.
Liverpool were beaten 4-2 by Aston Villa last time out, but can still finish above the Europa League winners in fourth if they beat Brentford in the final game and Unai Emery's men lose to Manchester City.
That being said, even if they do end the season on a high, Foot Mercato believe that "the tide is turning quickly" at Anfield, and he could be axed from the role.
According to the report, Iraola is the man sporting director Richard Hughes wants to replace Slot, having previously acquired the Spaniard during his time at Bournemouth.
Iraola will leave the Cherries after leading them to European qualification, with the same article claiming that Liverpool internally like his "modern yet discreet profile".
The Reds will have to move quick to land the 43-year-old as Crystal Palace have already made contact and many European clubs are bound to be interested.