Ter Stegen will miss the rest of the 2024-25 campaign with the severe knee injury that he suffered during Barcelona's 5-1 victory over Villarreal in La Liga last weekend.
Barcelona are expected to bring in a replacement in the near future, and it is being reported that Szczesny, who is available on a free transfer, is their leading target.
According to SPORT, the experienced goalkeeper is 'close' to making the move to Camp Nou as Ter Stegen's replacement.
The 34-year-old made 252 appearances for Juventus between 2017 and 2024 before departing in the middle of last month, with his contract in Turin being terminated by mutual consent.
Szczesny 'closing in' on Barcelona move
However, his proposed move to Barcelona has been complicated by the fact that he could owe Juventus €2m (£1.7m) if he joins the Catalan outfit on a deal until the end of the season.
Szczesny was allegedly paid around €6m (£5m) by Juventus over the summer as part of his departure, with the goalkeeper expected to retire, and he could have to repay a third of that if he returns to the field.
When questioned on the situation by Mundo Deportivo, the goalkeeper said: "I just hope that Marc recovers soon. He is a good friend and a great goalkeeper and I wish him the best. That's the only thing I can comment on."
Meczyki report that the ex-Poland international will make a final decision 'in the next few hours', with a deal then potentially being signed for the rest of the campaign.
Pena will start against Getafe on Thursday
Inaki Pena will be between the sticks when Barcelona return to La Liga action against Getafe on Thursday, and the Catalan club's head coach Hansi Flick has insisted that he has "full trust" in the 25-year-old goalkeeper.
"Inaki is doing very well, he is very professional and has trained very hard. He is focused, despite being an assistant coach. We trust him," said Flick ahead of the clash with Getafe.
"We will see what we do, we also have very young players in defence. At the moment, we do not feel under pressure and we trust Inaki."
Former Barcelona goalkeeper Claudio Bravo has also offered to come out of retirement if he is wanted by the Catalan giants, although he is not thought to be a serious option at this stage of proceedings.