The 18-year-old has already been the subject of three unsuccessful bids from Bayern Munich as they look to freshen up their squad with some new faces, while a fourth bid with matched Chelsea's £35m asking price is still being weighed up in west London.
Chelsea will still decide the destiny of Hudson-Odoi, but with only 18 months left on his current contract, the Premier League club may decide that the offer from the German champions is too good to pass up.
Chelsea are yet to comment on rumours that Hudson-Odoi could be sold but, writing for the Daily Mail, pundit Sutton was impressed.
"To stay here is better for him", Sarri said. No because I am not in charge of these questions and don't want to speak to a player on something that doesn't depend on me.More news: Peyton Manning recommended Adam Gase to Jets
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Bayern's latest bid is believed to meet Chelsea's valuation of the player.
Chelsea will take on Tottenham Hotspur in the EFL Cup semi-final first leg at Wembley on Tuesday and the Chelsea boss should put money where his mouth is and name Callum Hudson-Odoi in the first XI.
"I don't think (he should move to Bayern) because he's an English player", Sarri told reporters on Monday.
"I saw him every day in training and he was really very normal".
Chelsea are a club often criticised for their approach to young players, and bringing through new talent. He can play but of course, sometimes he will be on the bench, like Willian or Pedro, but now I can start to consider him at the same level.