The Poland internationals both left The Emirates Stadium prior to Wenger's exit after 22 years in north London.
Fabianski moved to Swansea City in 2014 before joining West Ham, while Szczesny spent two years on loan at Roma prior to completing a permanent switch to Juventus.
Between them they made over 250 appearances for Arsenal during their respective spells under Wenger, and owe plenty to the Frenchman.
However, that has not stopped them from doing impressions of the coach, who turned 69 last month.
The players were recounting when they told Wenger they wanted to leave Arsenal, with Szczesny leaving a letter on his desk.
And mimicking Wenger's dour tone, both players said in an interview with Polish website Onet: "Well Lukasz, I want you to stay but you can go."
Szczesny then followed the impression with a story regarding Carl Jenkinson, who had a nightmare start to his Arsenal career upon joining the club from Charlton in 2011.
Just a month into his spell the then 19-year-old netted a spectacular own goal from 25 yards, looping a volley over Szczesny in a 2-1 Arsenal win at FC Cologne in a pre-season friendly.
At half-time, Wenger's right-hand man Boro Primorac approached the defender but instead of consoling the teenager produced a hysterical one-liner.
The Juve stopper said: "When Carl Jenkinson had his debut. Carl is a turbo-fan of Arsenal, there were those photos of his room, quilt, posters.
"He came to Arsenal when he was 22 and he played in a friendly game vs Koln.
"In [the first] 45 minutes he scored an own goal from 25 yards, you can't imagine. A volley right in the corner.
"And he was in a horrible mood at half-time, sitting depressed; tears in his eyes.
"Then Boro [Primorac] comes over to him, you know in a friendly game, and his words: Carl, congratulations on your first goal for Arsenal!"
Jenkinson's Arsenal career has barely improved since that humiliating incident, with a regular first team place hard to come by both under Wenger and new boss Unai Emery.
In nine seasons at the club he has made just 155 appearances and had two loan spells at West Ham and one with Birmingham City.
He has made just two appearances this term, in the Europa League against Sporting CP and the Carabao Cup against Blackpool.
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