The forward has been linked with a move to Manchester United and Barcelona, but Sarri said he was not concerned that his delayed arrival had anything to do with engineering a move away.
"We tried in our short time together to review what we have done, analyse a little bit what Chelsea will be to try and see what we have to do, and play the final".
"I talked with him yesterday", Sarri said on Friday when asked about the player's future. I'll be happy if we arrive at the end being there [in contention] in April and May.
Jorginho, admittedly, was one hell of a signing, and acquiring him ahead of Manchester City was a huge coup.
"The table of the last Premier League told me City 100, Chelsea 70 points", he said.
"Always Chelsea is a big rival".
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City had been ambushed and the frustration for the Premier League champions is that Jorginho surely would have been lining up for them in Sunday afternoon's Community Shield if Chelsea had replaced Antonio Conte with someone other than Sarri.
In each of the past two Community Shield matches, new signings have scored, with Zlatan Ibrahimovic netting for Manchester United against Leicester City in 2016 and Sead Kolasinac doing likewise for Arsenal a year ago.
"But deals are deals, agents are agents and players are players, so I don't know what is going to happen". Manchester United beat them 3-2 in 2011 and Arsenal beat them 3-0 four years ago, two years after City beat this week's opponents 3-2 at Villa Park.
"You know, try be fair with what I see on the pitch and off the pitch, and try to choose the right line-ups, win games and try game-by-game to do our best".
After finishing fifth last season, Chelsea might have been expected to be more active in the transfer market this summer.
The City winger's disappointment was compounded as the defending champions lost to Mexico and South Korea, going out at the first stage of a World Cup finals since 1938.
While neither side will be at full strength due to the hangover of the World Cup, take a look at our top three Chelsea vs Man City predictions below.