The 22-year-old has recovered well from the disappointment of a summer in which he was not selected in Germany's World Cup squad and then returned to England to discover he had lost his starting place under Guardiola.
Sane has still only started seven of City's 14 league games this season but four goals in his past five Premier League games suggests he is rediscovering his impressive form of the past two seasons.
And even though Sane is yet to join a list of senior stars such as Sergio Aguero, David Silva, Kevin De Bruyne, Raheem Sterling, Ederson, Gabriel Jesus and Nicolas Otamendi in signing new long-term contracts with the club, Guardiola is convinced that will happen.
"I don't have any info about the club, about being in trouble with Leroy," said the City manager, whose side travel to Watford on Tuesday.
"The last info I had was that it's going well but the process is not one day -- Raheem Sterling it was not one day. Except Kevin De Bruyne, it was in one or two days done, the other ones sometimes take longer but hopefully he can stay here for many, many years." Sane's task at City this season has been further complicated by the summer club-record signing of ?60 million ($76 million) Leicester winger Riyad Mahrez.
- Mahrez v Sane -
The pair have been effectively engaged in a straight fight for the wide left position in Guardiola's attack, with Mahrez having made one less start than Sane but having been involved in one more league game when substitute appearances are factored in.
But it is clear that Sane, who became a father for the first time earlier this year, has noted the warning signs and improved his form of late for the Premier League leaders.
"I'm pretty sure becoming a father helps in many senses," said Guardiola. "I think he was incredible last season, he played a lot of games because we had just one left winger, and he had an incredible season, but we'll see.
"There are many games to play and I have a feeling he can do better. In many things he can do better, but with the age he has and the potential he has we are delighted to have him here."
The City manager, blessed with an embarrassment of riches in virtually every position, admits that team selection is one of the most difficult aspects of his job.
But the competition for places has also ensured that his players have maintained an unbeaten start to the domestic season and form that has them on course to eclipse even last season's record-breaking championship campaign.
Guardiola has not ruled De Bruyne, who has played just 81 minutes of league football this season due to two knee injuries, out of the weekend visit to Chelsea. "He's started training. It's day by day," he said.
"This kind of situation, if the player himself decides it feels good, he will train with the team. We will see.
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