The Manchester City boss confirmed the approach after the 4-2 FA Cup triumph over Eriksson's Leicester side which booked a fourth round trip to Meadow Lane.
Eriksson called Mancini, who was out of work at the time, to discuss a position at County, whose own financial state had not yet begun to unravel.
"He tried to get me to manage Notts County," Mancini said. "We spoke about it one or two times but then we finished.
"When we spoke, it was a good situation. Afterwards it wasn't, so I am happy to be here now."