Despite the successful exploits of number two Stefan Ortega, Ederson remains Guardiola's first-choice shot-stopper and has held that position for seven years now.
However, the former Benfica goalkeeper is a serious target for teams in the Saudi Pro League, and he is thought to be willing to take on a new challenge this summer.
Al-Nassr reportedly tried and failed with a bid to sign Ederson, and they are unlikely to go back in for the 30-year-old after capturing Athletico Paranaense's Bento.
There is still the possibility that one of the other Public Investment Fund-backed teams could make an approach, though, and Ederson is now in the final two years of his Citizens deal.
Guardiola unsure whether Ederson will stay
The 30-year-old was on the bench for Man City's first game of pre-season, a 4-3 defeat to Celtic in the United States on Tuesday night, although he replaced backup Ortega for the second 45 minutes.
City were 3-1 down by the time Ederson came on before pegging the game back to 3-3, but a 68th-minute strike from Luis Palma decided the contest in Celtic's favour.
Following the seven-goal spectacular, Guardiola was quizzed on Ederson's future by the press, and the Man City boss insisted that no official offers had arrived for his number one.
However, the former Barcelona head coach also admitted that the Brazilian's next career move would also hinge on the activity of other clubs, even though he would like to keep him around.
"I'd like him to stay but it depends on other clubs. I don't know the situation. There have been no contacts in the last days. It's a question of training, being with us until the transfer window finishes and we'll see," Guardiola said.
Ederson has established a reputation as one of the best modern goalkeepers in the world during his time at the Etihad, in particular excelling with his footwork and distribution under Guardiola.
The 30-year-old has won six Premier League titles in Manchester, as well as a Champions League, Club World Cup, UEFA Super Cup, two FA Cups and four EFL Cups, and he boasts 155 clean sheets from 332 competitive games in all tournaments.
What has Guardiola said about Kevin De Bruyne's future?
Ederson is one of two Man City stalwarts on the radar of Saudi chiefs, who are also dreaming of bringing Kevin De Bruyne - out of contract in the summer of 2025 - to the Middle East.
While Guardiola could not give a firm answer on Ederson's future, the City boss insisted that De Bruyne would not be leaving this summer, even though he would walk away for nothing next year.
Man City's next friendly match sees the Premier League champions travel to New York City to meet AC Milan on Saturday.