Following England's heartbreaking loss to Croatia after extra time in the semi-finals of the epic footballing tournament that has been Russian Federation 2018, the pair got into a right old ding-dong in the TV studio.
"Roy Keane is back with us to restore some calm".
But Wright, clearly a little emotional after the nerve-shredding defeat to Croatia, was not intimidated by the Irish hardman's reputation.
Wright, sat alongside fellow ex-England internationals Gary Neville and Lee Dixon, fired back: "Why shouldn't we get excited about it?" You were planning the final where the parades were.
"You're talking about the final?" "Roy Keane trying to keep the grin exploding from his face all over every front room in England", he said.
"I made the point a few weeks ago, I know a bit tongue-in-cheek but you have to focus on one game and football's coming home".
One tweet read: "Roy Keane, you never got anywhere f***ing near aWorld Cup final".
Keane added: "And I was right". "You need a reality check".
"We weren't talking about the final, we were just having a laugh with you".
One said: "You could learn from Roy Keane, try being open and honest and telling the truth".
Neville found the whole thing piss-funny. It's something to get excited about. It was the semi-final, group matches.
The game was then decided late into extra-time when Juventus star Mario Mandzukic broke the hearts of a nation and sent Gareth Southgate's men home.
Ultimately accusing them of not showing enough quality, Keane believed the inexperience of their players, and a lack of trophies won by the players in their club careers, told throughout: 'It was a step too far for them'.
The Three Lions looked set for a World Cup final when Kieran Trippier netted a sensational free-kick inside 5 minutes.
Let's hope Wrighty and Keano are sat next to each other on the plane home from Russian Federation.