The world’s oldest football club, who were recently taken over by a Middle Eastern consortium, and Eriksson’s agent Athole Still, are however refusing to comment on his involvement.
The Swede was sacked from his role as coach of the Mexico national side in March, following an unsuccessful 2010 World Cup qualifying campaign.
County only narrowly avoided relegation from League Two (fourth division) last season, but Middle East investors Munto Finance Ltd have made it clear they have ambitious plans for the Nottingham club which was founded in 1862.
Ian McParland will remain as manager and Eriksson will be appointed in a senior role, to be officially revealed on Wednesday, according to reports.
The 61-year-old had also been linked with the Swedish national team and with Portsmouth.