Current coach Lars Lagerback, who has led the Scandinavians to the last five major tournaments, is set to quit following a disastrous World Cup qualifying campaign.
They are only a point behind second-placed Portugal in Group One, but their rivals play at home on Wednesday against a Malta side who have lost eight and drawn one of their nine matches.
It has immediately sparked a campaign in Sweden for Eriksson to be put in charge as the overwhelming favourite in newspaper polls back in his homeland.
However, a spokesman for the Swedish FA said: "The national team's qualification campaign still has a match remaining and a shortlist has not yet been drawn up."
Former England boss Eriksson has previously suggested he would like to lead his country before retiring.
He refused to answer questions from Swedish journalists about the national team following Notts County's 2-2 home draw against Torquay yesterday - a result that signalled the end of Ian McParland's reign as manager at Meadow Lane and which could see Eriksson take charge of first-team affairs for the Magpies' game against Rotherham at the weekend.
However, his trusted right-hand man Tord Grip told the Daily Mail: "I don't know if he has a clause in his contract, but I'm sure he would be interested, I think.
"Then we'll see if it is the right time, but, at the moment, I don't know. We must wait to see what happens."