The English Football Association responded to the reports on Monday night by confirming talks had been held with a view to him taking over.
The Ansa news agency said the Serie A coach has signed a contract "of several years", worth around £1.8 million, with the FA and will take the national team hot-seat from 1 July 2001 after his contract with Lazio expires.
If confirmed, the Swede would be the first foreigner to take the job.
FA executive director David Davies said: "Meetings have taken place over the past 24 hours with Sven Goran Eriksson and representatives of his club, Lazio.
"The FA have discussed the possibility of him taking charge of the England team both for key games in the short-term, and in a full-time capacity in the long term.
"Those talks will resume in the near future."
Eriksson failed to confirm or deny the reports, stating that he was obeying club policy of not speaking to the press unless it was about information concerning forthcoming Champions League fixtures.
Ansa quoted Eriksson as saying: "I'm not talking to the media."
Meeting
The agency said an FA delegation met Eriksson on Monday at the Formello training complex after Lazio's new signing Dino Baggio was presented to the press.
Eriksson began to take a training session and was then called over by club vice-president Dino Zoff and director general Massimo Cragnotti, son of Lazio president Sergio.
He was then led to a room for a meeting with the FA delegation and Sergio Cragnotti and a deal was swiftly concluded, said Ansa.
Davies added: "We are continuing to build a team of young English coaches, all with real potential, to work with the new senior England coach.
"Our aim is to get the best available team of coaches to give the England players the greatest chance of success in international competition. That's what the supporters want and what the country wants.
"We are determined to achieve that objective."
Leicester City manager Peter Taylor is in charge of the England team for the friendly against Italy in Turin next month on a temporary basis.
Arsenal boss Arsene Wenger along with FC Copenhagen coach Roy Hodgson were the other front-runners for the vacant England manager's position.