"An offer has been made, negotiations are under way," a spokeswoman for the federation said.
Swede Eriksson, 64, has served as technical director of Thai club BEC Tero Sasana since September.
He has also managed AS Roma, Manchester City and Benfica.
Ukraine's previous boss Oleg Blokhin resigned in late September after failing to lead the team out of the group stages in the European championship, which Ukraine co-hosted this year, and accepting the job of head coach at Dynamo Kiev.
Ukraine had earlier approached English club manager Harry Redknapp with a similar offer.
Redknapp subsequently took over as manager of Queens Park Rangers.