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A host of names have been linked with the Anfield job in recent months, most notably Xabi Alonso and Rúben Amorim.
But Feyenoord boss Arne Slot is the leading candidate and the Daily Mail reports that talks are well underway between the two clubs, and could even be finalized in the coming days.
Slot has done a fine job at Feyenoord since arriving in 2021 from AZ.
He reached the Europa Conference League final in his first season in charge and followed that up by winning the Eredivisie last term.
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His side is on course to finish second this time around, with Slot well-liked by his players.
Speaking to Colney Carpool, Nelson said: "Arne Slot is a great manager.
Moroccan winger Oussama Idrissi played under Slot at AZ before reuniting at Feyenoord, after signing on loan last season.
Speaking to Dutch newspaper AD last year, Idrissi was asked where Slot ranks alongside the likes of Ten Hag: "For me, he is the best.
Of course, but I think Arne Slot is perhaps one of the better Dutch coaches at the moment.
"I think the way he plays and the philosophy he has means he could be a Liverpool coach.