Richards was on duty with the Man United legend for Sky Sports' coverage of Liverpool vs Man City where the banter was flowing in the direction of Keane after his famous dispute last week.
After being confronted with an angry Ipswich fan, Keane went viral for telling the supporter that he would 'see him in the car park' after the match.
After the 2-0 win for the Reds, Richards shared a picture from the car park at Anfield with Carragher and Keane looking at their watches.
Richards wrote: "This Ipswich fan is really taking his time. We just want to go home Roy," with a winking emoji.
Keane was clearly up for being part of the joke just hours after he was on the end of more banter in the Sky Sports' studio.
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Mohamed Salah and Virgil van Dijk did a live interview with David Jones and the pundits in which Gary Neville decided to give the player of the match award to the Dutch defender.
Smiling, Van Dijk joked: "I'm surprised Carragher wouldn't give it to you," as he addressed Salah.
The Egyptian forward then laughed, where he replied: "Oh, he wouldn't. Never. He wouldn't give it to me! I don't want to talk about this!"
It came after Carragher labelled Salah 'selfish' for shifting focus onto himself amid his ongoing contract situation.
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After the interview, Jones turned to Carragher and asked for his thoughts, to which the former defender joked that he would meet Salah 'in the car park'.
Richards then added: "Stood next to Roy!
Host Jones then commented: "I don't know what they are talking about Roy, it seems unfair," to which Keane simply smiled and stayed and quiet.
It hasn't been a good week for Keane, who was also the subject of a joke by comedy legend Ricky Gervais.
Announcing Gervais as the special guest for The Overlap, Carragher commented on X, saying: "Bloody loves football, @RickyGervais."
That led the comedy star to reply: "I'm just glad Roy didn't want to chat to me in the car park."
It came on the day that goals from Cody Gakpo and Salah secured a 2-0 win for Liverpool over Man City.
That victory put Arne Slot's side nine points clear at the top of the table and extended their lead over Pep Guardiola's side to 11 points.