The Dane is free to sign a pre-contract agreement with foreign clubs with his current deal set to expire at the end of this season.
A new contract from Chelsea has been on the table for some time, but Christensen has finally rejected the offer.
According to Cadena SER, via Sport Witness, moving Barca is considered a 'real option' for Christensen.
The 26-year-old could be ready for a new challenge after spending almost a decade at Stamford Bridge.
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