The La Liga outfit are keen to keep hold of the Netherlands international for another season, with head coach Xavi delighted with his contribution.
The report claims that the Catalan club want to sign De Jong on the same salary with no fee, and it will be up to Sevilla to decide whether they are prepared to agree to another season.
The experienced forward scored the winner in Barcelona's 3-2 league success at Levante last weekend but could not help the club beat Eintracht Frankfurt in the Europa League on Thursday.
De Jong's current deal with Sevilla is due to run until June 2023.