England teammates Rogers and Rice were involved in a furious bust-up in the clash between Arsenal and Chelsea over the weekend as things got heated during the Gunners’ 2-1 victory.
Rice seemed to trip Rogers, leading to the England teammates pushing and grabbing at one another, with Rice controversially escaping a yellow card.
Despite Arsenal’s perfect start, Rice has struggled so far this season and has failed to make as much of an impact under manager Mikel Arteta as he normally does.
Speaking on Piers Morgan's Football Uncensored show, Souness believes that Rice cannot be considered an elite midfielder due to his defensive positioning.
"How many times do you see him as the last man with the ball? In the build-up, he's last man. He's sitting between two centre-halves or between the centre-half and the full-back. He's last man. A lot of the time, he doesn't play in midfield.
"In my second or third home game (of my career), I went into the back four like all midfield players do today. It's old man's football. It's cheating. An old man's way of playing midfield. You get the ball under no pressure and you play it out to the full-back.
"He (Rice) plays too deep to affect the game. I don't think he's got enough football. Let me tell you what he can do. He's the best defensive midfielder in the country right now, he smells danger. But then again, he's back there all the time."
Souness continued: “But modern players are a bit precious. Criticism doesn't fall easily on these (players') shoulders. He isn't the complete midfield player."
Since joining for around £105 million, Rice has been integral to Arsenal, but Souness may be right in saying that the midfielder must push forward if he is to make more of an impact on the pitch.