United are set to finalise a deal with Christiansen in the next 24 hours, securing their replacement for Garry Monk after a three-week search.
Christiansen was approached for talks by United owner Andrea Radrizzani after taking APOEL to the last 16 of the Europa League this season.
The 44-year-old, whose playing career started at Barcelona, parted company with APOEL on the same day that Monk resigned as Leeds head coach.
APOEL chose not to renew Christiansen’s 12-month contract despite him taking the Cypriot club into the Europa League’s knockout stages and winning Cyprus’ first division title.
His side topped their Europa League group ahead of Olympiakos and reached the last 16 for the first time after beating Athletic Bilbao over two legs, eventually losing to Anderlecht.
APOEL released him in the wake of a defeat to Apollon Limassol in the national cup final.
Christiansen’s previous management job was a two-year stint at another Cypriot club, AEK Larnaca, between 2014 and 2016 but Radrizzani moved to name him as Monk’s successor after interviewing Christiansen last week.