Nominations for the position, announced on Friday, include Britains David Nabarro - who was the United Nations special envoy for Ebola during the crisis in 2014/15 - and Ethiopias foreign minister and former health minister, Tedros Adhanom Ghebreyesus.
Also nominated are Sania Nishtar, a former minister in Pakistans government; the French former health minister Philippe Douste-Blazy; Italys Flavia Bustreo - currently an assistant director general at the WHO; and a former health minister of Hungary, MiklÃ³s SzÃ³cska.
In a statement the Geneva-based WHO described the director-generals position as that of a "chief technical and administrative officer" who oversees the agencys international health work, Reuters reported.
Chan, who was appointed in 2006, has come under fire for the WHOs slow response to the deadly Ebola epidemic which raged through West Africa in 2014/15, killing more than 11,300 people.
She will step down on June 30, 2017, making way for the new director general to take over.
The WHOs election process states that by January 2017, the agencys executive board will shortlist a maximum of five candidates.
They will be interviewed by the board, which will nominate up to three to go forward to the World Health Assembly in May 2017, where the WHOs 194 member states vote for a winner.