The Dutch central midfielder has failed to hit the expected heights since joining the Catalan giants from Ajax.
The 24-year-old is a regular starter, but his performances are often middling, which is leading the club to consider cashing in on him.
According to El Nacional in Spain, Chelsea have put in a bid of £33 million, while Barcelona want £50 million.
The report states that a compromise figure of £41 million may be enough to take De Jong to Stamford Bridge.
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