The Swedish football association (SvFF) today admitted they had made contact with Eriksson over the weekend regarding the coaching position vacated by Lagerback after he failed to guide the team to next summer's World Cup finals.
Jonas Nystedt, head of communications at the organisation, said that Eriksson was part of a shortlist of "five to 10 names" which also includes Fulham manager Roy Hodgson amongst others.
"Last Thursday, after the Albania game, the board had a meeting and discussed what route should be taken," Nystedt told Press Association Sport.
"Things that were discussed were, obviously, who it should possibly be, their education and career, reputation and location and things like that.
"There is a special list of five to 10 names and Sven-Goran Eriksson is on that list.
"What the Swedish FA did over the weekend was to contact a lot of these people, not just Sven-Goran Eriksson but a lot of people.
"We asked them what their situation was - like what it says in their contract with their club - and whether they were interested in the job.
"Sven-Goran Eriksson has been contacted but he is only one person on the list. Obviously the rules stipulate that we would have to discuss with Notts County the situation regarding Sven-Goran Eriksson in more depth."
He added to Sky Sports News: "Roy (Hodgson) is also part of the Swedish football family. I think that he is on the list, but there are also Swedish names and European names on the list.
"So you will have to wait and see."
Negotiations with Eriksson will likely to rely heavily on his ties to Notts County, where he took over the role as director of football in the summer, although the club today intimated they would not stand in his way should Sweden offer him the post.
The former England boss has previously said he was committed to his five-year deal with the League Two club as they ambitiously seek to rise through the Football League following Munto Finance's takeover in the summer.
Nystedt admitted the prospect of the 61-year-old splitting the roles would likely be discussed, although he added that the SvFF - who have installed a three-man team to find a new manager - would like to have the new man in place ahead of a pair of friendlies in the middle of next month.
"That (splitting the role) is one decision that they will have to take," Nystedt said.
"You look at the past we have had full-time coaches for Sweden, but I don't know what their decision will be.
"We will have to wait and see what comes from the negotiation, if even it gets to a point where there are negotiations with Sven-Goran.
"I have heard the president say that it could be done very quickly or it could take some time.
"That will depend on the name they pick. We play some friendlies in November and it would be nice if the new coach takes control of these games.
"But it is the group's job to answer that question."
Eriksson's business manager Lars Sternmarker told Swedish newspaper Aftonbladet that discussions with SvFF president Lars-Ake Lagrell, who heads the three-man team, would continue.
"Lars-Ake has spoken to both me and Svennis although I cannot reveal what was said for confidentiality reasons," he said.
"But Svennis is Swedish at heart and feels very happy and flattered."
Asked whether he thought Eriksson would take the job, Sternmarker added: "The federation has identified a number of options, and the fact they have called Svennis is not particularly strange since he is the most successful coach in Sweden.
"The purpose of these calls is to allow the federation to look over the possibilities, options and what the person himself wants.
"We cannot give any definite answers for a while, we think it's fun that a dialogue has been opened and that there is scope for more discussions."