A soft start with Huddersfield, Arsenal, Newcastle, Bournemouth, Cardiff and West Ham in his first six Premier League games have helped Sarri settle in.
Sarri has repeatedly insisted his side can't yet be compared to City or Liverpool in their third full seasons under Pep Guardiola and Jurgen Klopp.
"We have started to work together 40 days ago. So for us I think it is a bit early. We have to work, we need to improve and then maybe, in one year, we will be at the same level of Liverpool," said the Italian.
However, his transformation of Chelsea's style from the cautious approach of Antonio Conte to a side that asphyxiates opponents by dominating possession has been so seamless, a title challenge can't be ruled out.
"The biggest change I ever saw in such a short space of time. Wow. Style completely different. What a manager he is, to be honest," said Klopp admiringly this week.
United face Hammers with all eyes on Pogba
Jose Mourinho's relationship with Paul Pogba plummeted to new depths this week and all eyes will be on the Manchester United teamsheet at West Ham on Saturday for the latest chapter in the saga.
United — already eight points behind leaders Liverpool in the Premier League — give the impression they are lurching from game to game and on the cusp of a full-blown crisis.
The team appeared to have turned the corner after an indifferent start to the season with three away wins on the bounce but a draw against Wolverhampton Wanderers and a shock League Cup defeat on penalties to Championship side Derby have set alarm bells ringing.
Hazard dazzler ejects Liverpool from League Cup
The Pogba factor is the big talking point but there are plenty of other issues to give United fans sleepless nights ahead of the game against newly resurgent West Ham.
United boss Mourinho stripped Pogba of the vice-captaincy this week after the French World Cup star said the side should attack more, an implicit criticism of perceived negative tactics.
Mourinho, speaking after Tuesday's League Cup exit, for which Pogba was rested, said there was "no fallout at all, no problem at all" regarding the decision.
But it does not look like that.
Emery eyes seven wins in a row with Arsenal
Unai Emery believes restoring Arsenal's confidence has been the key to his side's revival as they look to make it seven successive wins when they face Watford on Saturday.
Pogba no longer United captain, says Mourinho
When Emery took charge at the Emirates Stadium in the close-season, the Arsenal manager found his squad's morale was at a low ebb after the disastrous final years of the Arsene Wenger era.
Emery's job was to restore his players' belief, while convincing them to buy into his football philosophy of high-tempo pressing from all areas.
Initially, it seemed the former Paris Saint Germain boss was struggling to get his message across as Arsenal were swept away by champions Manchester City on the opening weekend before squandering a two-goal comeback in a 3-2 defeat at Chelsea.
Hard-fought away wins at Cardiff and Newcastle maintained the momentum and by the time Arsenal eased to a 3-1 victory over Brentford in the League Cup third round on Wednesday, the north London club's winning streak had grown to six matches.
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