The Poland international is expected to feature in the FA Cup quarter-final at Manchester United on Monday night, provided he recovers from the virus which stopped him from being on the bench for the midweek Barclays Premier League win at QPR.
Szczesny, 24, has not started a league game since the 2-0 defeat at Southampton on New Year's Day, where he was culpable for the goals and afterwards was also caught smoking in the showers
That indiscretion resulted in a fine from the club.
Despite Colombian David Ospina making the most of his opportunities in recent weeks, Wilson, part of the Gunners' 1971 league and FA Cup-winning side, still believes 6ft 5in Szczesny has what it takes to cement a regular place between the posts once more.
"From the time Wojciech got into the Arsenal first team there were a lot who asked if he was good enough and I thought this boy has the potential to really be a solid, outstanding goalkeeper, I still believe that because he is - for his position - still relatively young," Wilson, 73, told Press Association Sport
"All I would a say to him is 'look, Arsenal is one of the greatest football clubs
If you go from here I am not sure you are ever going to get a club as good as this
At your age now you need to dedicate yourself to being the best you can be, to the exclusion of a lot of other things in your life'."
Wilson recalled: "I was a very late starter, but once I was in the Arsenal side, my family almost came second to my ambition.
"I devoted every moment to regular training and then when the boys went in for their bath, I stayed out (on the field).
"I wanted to make sure I never ever left the game saying I could have been better, so my message to Wojciech would be 'come on, prove how good you can be'."
Gunners boss Arsene Wenger is confident Szczesny, who has played in Arsenal's last two FA Cup ties, will be sharp if selected again.
"Wojciech is used to playing in big games and I think he will take that as a big challenge to show his quality," the Gunners boss said.
"He works very hard in training, so I don't think that will be a problem."
Arsenal head to Old Trafford in search for a first win there since September 2006, but on the back of good league form.
Wenger said: "We are the holders of the FA Cup, this competition is important to us and we want to go there to produce a result."
Source : PA
Source: PA