The shot-stopper has another two years left to run on his contract at the Emirates Stadium and there have been suggestions that he would like to depart.
There is concern at the club that Leno may not agreed to extend his contract, however Arsenal are still not looking to sell him.
It has been claimed that Arsenal are unlikely to sanction a departure for Leno this summer even if he does not sign a fresh deal.
Arsenal have been strongly linked with wanting to sign Ajax goalkeeper Andre Onana, while Newcastle United custodian Freddie Woodman and Brentford shot-stopper David Raya are mooted to be admired in north London.
Leno, 29, made 49 appearances for Arsenal over the course of the just concluded season and kept 16 clean sheets in the process.
The goalkeeper has now moved on to a total of 117 outings for the Gunners since joining the club in the summer of 2018.
Leno has been included in Germany’s squad for this summer’s Euro 2020.