The Spaniard's present deal is due to expire at the end of the current season.
If confirmed, the new agreement would take Guardiola's tenure at the Etihad Stadium to 10 years.
The club did not comment when contacted by the PA news agency about the reports which emerged on Tuesday evening.
Guardiola, 53, has won 18 trophies, including six Premier League titles and the Champions League, since taking charge at City in 2016.
Pep Guardiola celebrates with the Premier League trophy after Manchester City's 2023/24 triumph. (AP PHOTO)
Speculation over Guardiola's future, rife for several months, had increased considerably after the club confirmed recently director of football Txiki Begiristain would be leaving at the end of the season. Begiristain, a long-time colleague of Guardiola, is to be replaced by Sporting Lisbon's former Hugo Viana, a former Newcastle United player.Â
Ending uncertainty over Guardiola's position would prevent further disruption next summer at a time when the club are also due to compete in the Club World Cup.
The news, which reportedly could be confirmed later this week, would also come at a critical juncture in City's season. Hampered by injuries, the champions' form has wavered of late with the team having lost their last four matches in all competitions, the worst run of Guardiola's career.
It has also been a difficult campaign off the field with the club facing 115 charges for alleged breaking of Premier League rules following an investigation into their financial affairs.
Guardiola succeeded Manuel Pellegrini at City eight years ago after previous successful spells in charge of Barcelona and Bayern Munich.
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