The Arsenal goalkeeper has spent this past season on loan with AS Roma.
Szczesny has spent this past season out on loan at the Serie A side and he seemingly impressed enough to convince manager Luciano Spalletti he is worthy of another deal.
Roma have already signed goalkeeper Alisson for next season, but they are still keen to keep Szczesny in their squad.
Reports have suggested that they are keen on another loan deal for the Polish ‘keeper, but Arsenal are more interested in a permanent exit for their man.
At this stage then the two parties are far apart in their thinking, so they will meet this week to try to thrash out a deal for the player, according to Gianluca di Marzio.
The goalkeeper will return to London for the time being, with his future very much in the hands of Arsenal, who will need to be convinced into sanctioning another loan deal.
He has already made it clear that he would prefer to stay in Italy having criticised the Gunners in recent interviews, and will be praying that a deal can be struck.