The 30-year-old remains the Blues' first-choice stopper, but is coming under increased pressure from Thibaut Courtois, the Belgian loanee who continues to excel in Spain with Atletico Madrid.
Cech only recently signed a new contract that will keep him at Stamford Bridge until 2016, but there is a growing sense of expectation that Courtois could displace Chelsea's long-term custodian from the start of the 2013/14 campaign.
Gunners boss Arsene Wenger is ready to offer the Czech international an escape-route with the offer of regular first-team football at the Emirates Stadium, should he find himself demoted, and has sent Arsenal scouts to watch the Chelsea veteran on numerous occasions.
The fact that Wenger is preparing an audacious attempt to sign a player from direct Premier League rivals suggests that Arsenal will spend big again in the summer, with a goalkeeper high on the club's list of priorities.
Szczesny is fighting to save his Arsenal career, after he was dropped for last week's Champions League last-16 clash with Bayern Munich, with the returning Lukas Fabianski installed in his place for the impressive 2-0 win at the Allianz Arena.
Fabianski kept his place for Arsenal's 2-0 win away at Swansea in the Premier League on Saturday, and following back-to-back clean sheets, is likely to keep Szczesny benched.
Pepe Reina, Asmir Begovic, Victor Valdes, Rene Adler, and Michel Vorm are believed to be the other names on Arsenal's goalkeeping hit list, with a new arrival in north London a near certainty this summer.