The Englishman scored 185 goals in nearly 300 appearances for the Gunners.
This helped them to a Premier League title and two FA Cups.
He was managed by Wenger, who was honoured a a “Legend of Football” earlier this week, for two seasons.
And footage has emerged of the former forward sending a message to the 69-year-old.
Speaking on his Instagram channel, Wright said: “Listen, I just wanted to take this opportunity to apologise.
“It’s something that’s been bothering me for many years.
“I’m sorry that I went through the marble halls on rollerblades and bumped into you.”
This refers to the east stand of Arsenal’s former home Highbury where the offices were based.
“It wasn’t very professional,” Wright adde before using a mock French accent.
“In fact you said ‘Ian, this is not acceptable’.
“But hey, you got me a Premier League medal and that’s why I will love you forever.
The 55-year-old also expressed his apologies for not making the awards ceremony.
This footage was has been viewed more than 50,000 times since it was published yesterday.
And the Gunners were in stitches at the former forward’s admission.
“What a bloke – f***ing legend,” one supporter said.
Another commented: “Wrighty the trouble maker.”
While a third could not believe it, saying: “At first I thought the marble halls story was a metaphor, then I remembered you’re Ian Wright.”
But fans are not happy with current captain Granit Xhaka .