Guardiola was appointed City manager in the summer, the Spaniard taking up his first job in England after spells with Barcelona and Bayern Munich.
The former midfielder has long been linked with the England job, once ending a press conference when asked about the possibility of taking the job in September 2015.
But Manchester United legend Scholes has expressed his desire to see the 46-year-old manage the national team at some point in the future.
“I hope he becomes England coach one day and bring us his style,” Scholes told Marca.
“He can still succeed in England. He could improve in defence because at every ground you come under pressure, but everyone in England loves the way his teams play.”