Fomenko, 64, played for Dynamo Kiev as defender in the 1970s and has managed a number of Ukrainian clubs including Metalist Kharkiv, as well the Guinea national team in 1994.
Former England manager Eriksson, who visited Kiev last week with his agent and laid out the terms of a potential contract, was not present at the meeting on Wednesday.
Ukraine's previous manager Oleg Blokhin resigned in late September after failing to lead the team out of the group stages at the European Championship, which Ukraine co-hosted this year, and accepted the job of head coach at Dynamo Kiev.
Ukraine approached Englishman Harry Redknapp about the job but he decided to join Premier league club Queens Park Rangers.
- Sports & Recreation
- Dynamo Kiev
- Metalist Kharkiv