The Daily Mirror claims that manager Arsene Wenger has already offered Nasri a new double-your-money £80,000-a-week deal while the midfielder's agent insists he is happy to stay.
The move reflects the club's acknowledgment of the fine season the France international has had, and also comes on the back of a quiet transfer window for Arsenal.
The club's lack of transfer activity reveals Wenger's faith in his current set of players and illustrates a footballing philosophy based more on creating stars rather than shelling out astronomical amounts of money to buy them.
Arsenal's only foray into the maket in the January transfer window was signing Japanese teenage forward Ryo Miyaichi - the 18-year-old has been loaned to Dutch side Feyenoord for the rest of the season.
And the Daily Mirror believes Arsenal are keeping tabs on the "new Chicharito" - Omar Salgado, a 17-year-old striker with Vancouver Whitecaps.