The 24-year-old signed a five-year deal when he moved to the Etihad for a mammoth £35m transfer fee last June and has since become an integral part of Pep Guardiola's side, who boast a 16-point lead at the top of the Premier League.
According to The Sun, the Brazilian's impressive start to life in England has convinced the City hierarchy to act early and offer him an improvement on his current deal, which is worth around £70,000 a week in wages.
"The club is already looking at giving Ederson a new deal at the club," a source told the newspaper. "He was an expensive purchase but has been worth every penny. He has delighted Pep how quickly he's settled in.
"There is not a rush on him but the club will make sure he is looked after in the long term."