Hans Backe has left his assistant manager's job at Manchester City after just six weeks.
The Sun says the Swede left before Sunday's 1-0 win over Aston Villa for personal reasons and admits he may not return.
He said: "I am forced to quit because of illness in my family.
"I am now in Sweden and I cannot say at the moment when I can return to Manchester.
"This is hard to handle. But I don't want to say anything more."
Eriksson, who has known Backe for 20 years, said: "Hans has gone back to Sweden because of illness in his family. I cannot answer if he will come back."