The Gunners present goalkeeper, Wojciech Szczesny has not been consistent for the club, hence the club has decided to look out for his replacement during the transfer window.
With Szczesny's recent performance against Southampton being below par, where it was his errors, which led to both Saints goals, Wenger might think about signing a new goalkeeper.
Arsenal are aware of Cech's situation at Chelsea, as Cech has lost his starting place to the Belgian number one Thibaut Courtois after his splendid loan spell with Atletico Madrid.
As per the reports of The Daily Star, Arsene Wenger is ready to bid £7 million for the Chelsea goalie.
Would Jose Mourinho sell the player to a top rival club?
The answer might be yes, as £7 million sounds good business for a second-choice goalkeeper, though Mourinho may want to keep the player, especially since the Chelsea manager has sold third-choice Mark Schwarzer to Leicester City.
But, the story could have different had Manchester City come calling for Cech, as they are contenders for the Premier League title this season.
Cech is not the first goalkeeper to have been linked with the Gunners, as the club have reportedly shown interest in the highly-rated 21-year-old goalkeeper Loris Karius from FSV Mainz 05.
Karius has been dubbed as the "new Manuel Neuer," and a number of other clubs are also said to be interested. Benfica are also interested in the goalkeeper along with Borussia Dortmund and Valencia.
The Gunners need to act quickly during the January transfer window, as Liverpool are also on the lookout for a goalie to replace Simon Mignolet.
The Reds have been linked to Cech as well recently, so if a better offer comes in from Liverpool, Chelsea might not hesitate to sell the player to the Merseyside club.