The Euro 2024 finalists are on the hunt for a new man to step into the dugout after Southgate resigned eight years into the role.
In that time, he led England to the European Championship finals twice, a World Cup semi-final and restored a sense of unity in the camp following a period of discontent around the national team.
Several names have been touted to replace the ex-Middlesbrough boss, including Eddie Howe, Lee Carsley, Graham Potter and Mauricio Pochettino, but Eriksson has two other names in mind.
The 76-year-old became the first foreign coach to manage England in 2001 and believes the FA should consider heading down a similar route for their next appointment.
Speaking to The Telegraph, he said: “If he is English or foreign, I don’t think it should mean much.
After 102 games and almost eight years in charge, Gareth Southgate has announced he is to leave his role as manager of the #ThreeLions.
— England (@England) July 16, 2024
“You just have to find a top manager or a young one with a good future. If you want to aim high, the obvious two contenders are Jurgen Klopp or Pep Guardiola.
“They know English football, the players and culture. If there was even the slightest suggestion they were interested in the job, England should go for it.
“We are talking about two of the best managers in the world. Klopp is taking a break and I’m not sure whether stepping down from Manchester City is in Pep’s mind.
“But you have to aim high, and appointing either of those two would be a huge statement for England and their aims for the future.”
As mentioned by Eriksson, Klopp is taking a break from football after leaving Liverpool earlier in the summer.
He has already reportedly turned down the USMNT job and has no plans to pick up a new role anytime soon.
Guardiola remains committed to Manchester City but his contract does expire next year.
Reports have emerged suggesting the FA would be willing to appoint an interim manager if it means they could snap up the Spaniard when the time is right.