Having endured a mixed a season so far, the 22-year-old was dropped last month in favour of Lukasz Fabianski, who has gone on to concede just one goal in three games for the Gunners, including a clean sheet at Bayern Munich.
However, Seaman has challenged Szczesny to try to force his way back into the side and believes that the competition is good for the club.
"All goalkeepers make mistakes but the really good ones learn from them and show they are able to bounce back from a setback," Seaman told The Metro. "You have to recognise where you have gone wrong, admit you made an error and work hard to put it right. It's important to have a lot of self-confidence as a goalkeeper and you need to be strong enough to tell your defence when they have gone wrong. But you never stop learning and the best goalkeeper recognise that.
"I don't know if Szczesny will win back his number one spot. It's quite interesting with Fabianski doing really well. He's worked really hard since his injury and he looks totally different goalkeeper. But it's great to have that competition. It's important to show you have the right character to be back on track.
"Look at David de Gea at Manchester United, that's exactly what he has done. He had a wobble but was mentally strong and bounced back and now everyone is rightly praising him for being a great goalkeeper."
Seaman played 406 Premier League games for Arsenal while winning 75 caps with England.