Suarez, a £23 million signing from Ajax in January, scored on his debut against Stoke and has impressed in his other games, although he is cup-tied for Liverpool's Europa League campaign.
The Uruguayan forward will get another chance to shine when the Reds travel to London for their Premier League clash against West Ham at Upton Park on Sunday and Gerrard, who is also set to return to the side, has talked up his team-mate.
"Already we can see what a good player Luis is. He's got good pace and awareness and he's settled in very quickly,'' he told the club's official website. "He's a fighter too and the type of character he is means he's going to work really hard for the team.
"We've all been delighted with his first few performances. Hopefully there is even more to come from him too.
"I expect him to be even better when he adjusts to the speed of football in this country. He hadn't played many games in the weeks before he moved here so he's still getting his match fitness. When he gets that, he will be very difficult to stop."