The Spanish giants also want to increase his £53m release clause to stave off interest from a number of Premier League sides.
'The club wants to shield the French defender before offers from England, the club has already met with his representative to improve their contract and raise the clause,' says the Catalan newspaper.
Manchester United are one of those clubs interest in the Frenchman's services. Jose Mourinho had identified Umtiti as a potential replacement for summer signing Victor Lindelof, who has struggled for form since arriving at Old Trafford.
However, Barcelona have acted and will propose a new deal for the centre back in the coming weeks.