Neville is a Red Devils legend and made more than 600 appearances for the club in an illustrious career that spanned from 1992 to 2011.
He won 20 trophies during his time at the club, which included eight Premier League titles.
There is still plenty of affection for the former right-back at Old Trafford and one fan was even sporting a unique scarf in Neville's honour during their 3-0 win over Brentford on Monday.
The Sky Sports cameras panned to the man in question, and Keane and Carragher couldn't let the opportunity pass.
"There must have been a sale on," former Manchester United captain Keane said.
Host David Jones said: "I'm sure they'll catch on."
Liverpool legend Jamie Carragher added: "Gary Neville or Teabag?"
The Liverpool legend referencing that Neville has an uncanny likeness to the Prison Break character.
Keane had some very kind words about Neville later on in Monday Night Football, though, as he picked him in his all-time Manchester United XI.
The former midfielder said about the former England right-back: "Brilliant. He was a brilliant player.
"He was a brilliant character in a sense, he would go to bed at 8.30pm in the evening and we would criticise him. We all embraced Gary. Gary fell into the group, no problem.
"In fairness, when you get into the first team, Gary became more vocal. There's no stopping him now. Looked after himself. You have to have quality to do what he did."