The 37-year-old Cech responded to the reports by tweeting: "Despite the news today as I had already said to everybody before, I’ll make (a) decision about my future after the last game. Now my sole focus is to win the EL with @Arsenal".
Chelsea were not immediately available to comment on the media reports.
Former Czech Republic international Cech, who won 124 caps, spent 11 seasons at Stamford Bridge, winning the Champions League and Europa League, four Premier League titles, four FA Cups and three League Cups before moving to Arsenal in 2015.
Cech had previously announced that he would retire from playing at the end of this season.
Arsenal face London rivals Chelsea in the Europa League final in Baku, Azerbaijan on May 29.
(Reporting by Philip O'Connor; Editing by Ken Ferris)
