The Three Lions are without a full time boss after Southgate quit following their Euro 2024 final defeat to Spain.
The team is currently being managed by interim boss Lee Carsley, who was previously with the Under-21s.
"I think he would be great, he would be amazing," ex-Manchester United and Barcelona defender Gerard Pique told Express Sport at PokerStars' 20th anniversary of EPT Barcelona.
"He understands perfectly the Premier League and English football and I know he wants to be the manager of a national team in the future. I think it makes sense for Guardiola to be the coach of England."
"I think that they are knocking on the door and at some point the door opens," Pique added.
"I think they have a good team, had a good coach.
"I love English fans, how committed they are and how much they want their national team to win. But I think it has been so many years since they won the last time so I hope they can win it at some point."