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City are 11 points clear of nearest challengers Manchester United, are on a record run of 16 consecutive wins in England’s top flight and through to the Champions League knockout phase after comfortably winning their group.
Guardiola, 46, is half-way through his three-year deal at City but the club hierarchy are reportedly confident the former Barcelona and Bayern Munich boss can be persuaded to stay longer.
Guardiola said last month that he was happy at City and his contract, which expires in 2019, was “not a big issue”.
City failed to mount a serious title challenge in Guardiola’s much-hyped first season in England, finishing a disappointing third. They also exited the Champions League in the first knockout round.
But the club invested heavily in new players during the summer and look certain to romp away with the Premier League title even though the season still has five months to run.
The Times newspaper said there was an acceptance that when Guardiola arrived in Manchester last year he might not stay beyond his three-year deal but there is optimism he will make a longer-term commitment.
The report said Guardiola was enjoying working with chief executive Ferran Soriano and director of football Txiki Begiristain, both of whom previously worked at Barcelona.
Guardiola quit Barcelona in 2012 despite four trophy-laden seasons to recharge his batteries.
Following a sabbatical with his family in New York, he returned to management in Germany, leading Bayern to three consecutive Bundesliga titles before moving to City in 2016.
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