Federation officials met Eriksson in Kiev on Wednesday, it said in a statement, who together with his agent laid out the terms of a potential contract.
"The Executive Committee meeting will take place next week," - a federation spokesman said.
The federation added that they were also considering hiring local coach Mykhailo Fomenko.
Swede Eriksson, 64, has served as technical director of Thai club BEC Tero Sasana since September and 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 accepted the job of head coach at Dynamo Kiev.
Ukraine had earlier approached English manager Harry Redknapp with a similar offer.
Redknapp subsequently took over as manager of Queens Park Rangers.