The Ukrainian Football Federation has begun discussions with Sven-Goran Eriksson over their managerial vacancy.
The approach for the former England coach has been made after Harry Redknapp turned down their advances, opting instead to take over as the new manager of Queens Park Rangers.
"An offer has been made, negotiations are underway," a spokeswoman for the Federation told reporters.
Should Eriksson take the job, he will come up against England in a World Cup qualifier in September next year.
As well as England, the Swede has also managed Mexico and the Ivory Coast at international level.