The Gunners have been linked with a move for the 32-year-old Czech Republic international, but goal.com have reported that Arsenal have been told the have no chance of signing the player at the end of the season.
Cech has lost his place as Blues No 1 this season to Thibaut Courtois, who made his move permanent last summer after three campaigns on loan at Atletico Madrid.
An Arsenal source told Goal: "Cech is still one of the best goalkeepers around and he would be the perfect signing, but the message from Chelsea is not to bother wasting our time."
Cech has made only five appearances in the Premier League for the Blues this season, but he did start the 2-0 Capital One Cup final win over Tottenham Hotspur at Wembley last month.
Courtois, on the other hand, has started the other 26 league games for the club this season, plus five in the Champions League.
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