BBC Radio Leeds reports that the ex-Spain international, 44, is close to signing a deal to replace Garry Monk.
Christiansen led Apoel to the Cypriot First Division title and the Europa League last 16 in 2016-17 in his sole season in charge before leaving in May.
The former Barcelona striker will be the club's sixth boss since Brian McDermott left in May 2014.
His only other managerial experience is with AEK Larnaca, also in Cyprus' top tier, who he led from 2014 to 2016.
Monk left Elland Road in May after failing to agree terms on a new deal with new owner Andrea Radrizzani and was appointed Middlesbrough boss earlier this month.
Denmark-born Christiansen, who qualified to represent Spain through his mother, played in Spain, Greece, Denmark and Germany during his career and finished as joint top scorer in the Bundesliga while playing for Bochum in 2002-03.
More to follow.
Leeds United are set to appoint former Apoel Nicosia manager Thomas Christiansen as their new head coach.