Suarez was still yet to prove himself on the grand stage as he arrived from Ajax, but Gerrard recalled how he was impressed from his first sessions with the player.
“A lot of strikers that we used to sign did have respect for the likes of Jamie Carragher and other names around the squad but he (Luis Suarez) had no respect for anyone in training, in a good way," he said on BBC Sounds' Match of the Day: Top 10 podcast.
Adding further on the forward's training manner, Gerrard said: "He'd be backing into them [teammates], he'd be leaving a bit in on them, he'd have elbows up and I'd be thinking that's not normally what you'd see in training.
"You'd normally see a lot of respect but Luis would run through anyone and have a defender up the wall at any given moment.
"You knew straight away in days rather than weeks that he was going to be a top player for Liverpool."