The former Barcelona forward has won the Premier League and FA Cup since switching to Stamford Bridge from Camp Nou three years ago.
With Palace's opening game of their Premier League season away to newly-promoted Fulham in just one weeks time, they will need to move quickly should they want to secure his services for the start of the season.
Chelsea have come to an agreement with Pedro for the Spaniard to extend his contract by one season.
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This pre-season he already has two goals from three games. I want to stay here for 10 years.
"Now we face Manchester City in the Community Shield". I'd like for my players to have the personality to think that we are at the same level. It's a insane competition with a high level so I think every manager has the dream to come so he had the chance to come.
Reportedly due to a passport issue, the 29-year-old couldn't enter the country and earlier in the week, Sarri had stated that he wasn't impressed with his player's tardiness.
"I try to do my best every time I play and if he's watching then he's watching but I don't think about that". He said: "We'd love to have him back".
The Brazil-born Italy worldwide was also a top target for Guardiola, with the City boss admitting he thought a deal was as good as done.