Southgate announced his resignation after eight years in charge of the Three Lions last week, in the wake of their Euro 2024 final defeat to Spain.
Homegrown bosses Graham Potter, Eddie Howe and Lee Carsley have been touted as possible candidates to succeed Southgate, as has Mauricio Pochettino.
Reports have also suggested the Football Association could approach Guardiola with the intention of having him take over in 2025, when many believe he could step down as City boss.
While Guardiola has previously spoken of his desire to take an international job, for now, he is focused on City’s bid to win an unprecedented fifth straight English top-flight title.
“I’m really excited for this upcoming season,” he said during a press conference on Tuesday.
“I’m really happy here. Every season I need the break, definitely, but after that, I recharge my batteries and I have the same energy as usual.
“I know the competition is coming, and I am fully focused on that.”
City kick off their pre-season tour of the United States when they face Celtic in North Carolina on Tuesday, with fixtures against Milan, Barcelona and Chelsea to follow.