The clip of the Italian has been shared widely on social media, being viewed more than 1.5million times.
The tweet was captioned: "I knew Spurs were tight b******* but getting Conte to fly Ryanair is insane."
This caught the attention of the budget airline, who had their own response to the post.
Their Twitter account shared the video and said: "What do we think of Tottenham?"
This would have brought a smile for Arsenal fans as it is the start of one of their chants… with the reply usually 's***'.
It is not clear from the video exactly when it was taken, but the manager was flying back from Turin, according to @PhilippePaull who posted it on Twitter. Conte was back in north London for the first day of pre-season on Monday.
The Ryanair admin appears to be an Arsenal fan and is not the first time they've had a dig at north London rivals Tottenham.
When the club's former manager Jose Mourinho was hired by Roma, the Irish airline made a not so subtle insult to Spurs.
They tweeted: "Jose will be happy to know that we currently fly London to Rome from only £14.99.
"Due to his lack of trophies at Spurs, we expect a carry-on bag will suffice for this trip."