The Daily Express reports that Barcelona are keen to bring in the former Manchester United striker to provide cover for the injured Lionel Messi.
Reports claim Barcelona boss Gerardo Martino is intrigued by the technique and experience of the former United and Tottenham striker.
Barcelona are confident they can sign Berbatov for a nominal fee in January as the Bulgarian is out of contract at Craven Cottage at the end of the season.
Messi is expected to be out of action for up to eight weeks with a hamstring injury.
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