City and Liverpool are currently England's best two clubs headed by Pep Guardiola and Jurgen Klopp.
The two sides are separated by just a point on the Premier League table and both are into the last four of the UEFA Champions League.
Encounters between the two sides in the Premier League this season ended in frenetic 2-2 draws but Liverpool edged Sunday's FA Cup semi-final 3-2.
Their encounters often lack the feistiness that dominated the Arsenal-Manchester United rivalry of the early 2000's in which Keane was a constant fixture.
One of those encounters in the 2004/2005 season ended up with former United manager Sir Alex Ferguson having pizza thrown at him by a young Cesc Fabregas.
Keane appreciates the respect Liverpool and Man City have for each other but wants the dark arts thrown into the mix once in a while.
"The game has changed, and I think the standards they’ve set are amazing, fantastic," Keane told fellow pundit Jamie Carragher on LADbible TV's Agree to Disagree. "But you’d still like a bit more nastiness between the two.
"That was part of the game that I loved when I played against Arsenal, when Liverpool were having their challenges. I’d like a bit more needle between these two. Whatever the standard of football, and we can’t speak highly enough of these two teams, I’d like a bit more.
"People look back [at] United and Arsenal – a couple of sending-offs, fights in the tunnel, pizzas. We want to hear some pizza stories! It’s too nice, isn’t it?"
