Ukraine have been looking for a new boss since Oleg Blokhin resigned in late September, having failed to lead Ukraine out of the group stages at Euro 2012 even though they co-hosted the event.
And the 64-year-old Eriksson, who has been the technical director of Thai club BEC Tero Sasana since September, appears to be the leading candidate to take charge.
A spokeswoman for the federation said: "An offer has been made, negotiations are under way."
Eriksson is hugely experienced and was in charge of the England side between 2001 and 2006, leading them to the quarter-finals in two World Cups.
Prior to that he managed Benfica, Roma and Lazio, among others and, since leaving England, he has had stints with Manchester City.,Mexico, the Ivory Coast and Leicester.
Before they opened talks with Eriksson Ukraine had approached Harry Redknapp, but the former Spurs boss ended up taking charge at QPR.