Backe, who like Eriksson was on the shortlist to become the next head coach of the Sweden national team, has spent much of his managerial career in Scandinavia and has won four Danish titles with FC Copenhagen and Aalborg.
Asked if his move to Meadow Lane was finalised, he told a Swedish football website: "No, but everything suggests that will be the case.
"I fly to England on Monday afternoon and will meet with Notts County and read through the contract. If everything is sorted out, I will take over immediately.
"I've been thinking about it and came to the conclusion that I prefer to be a club coach. I have experience from the time in Mexico that you only have training every six weeks."