Germany international Ter Stegen underwent surgery after rupturing the patella tendon in his right knee during a 5-1 win over Villarreal over the weekend.
Szczesny, according to media reports, is expected to arrive in Barcelona soon to have a medical before signing a short-term deal.
"I have a lot of respect for Barca's history, it is one of the best clubs in the world," Szczesny told Spanish news outlet Sport on Thursday.
"I understand the difficult situation that has arisen for them after Marc-Andre Ter Stegen's injury and I think it would be disrespectful of me not to consider this option."
Barca manager Hansi Flick on Wednesday said their 25-year-old reserve keeper Inaki Pena is a potential replacement for Ter Stegen but they also need more experience.
"Inaki is 25, but the other goalkeepers are very young. We need more experience and that's why we're talking about it. We've talked about it and discussed it, and we'll have to decide," Flick told reporters after Barca's 1-0 win over Getafe.
Szczesny, who joined Juventus in 2017, announced his retirement in August after terminating his contract with the Serie A club where he had one more year left on his contract.
Szczesny retired with over 250 caps for Poland after helping Juve win three league titles and three Italian cups.
Barcelona are four points clear atop LaLiga with a perfect 21 from seven games and will next play at Osasuna on Saturday.
