The Uruguayan international has been in the headlines recently following a charge by the Football Association for allegedly making an offensive finger gesture to Fulham fans at Craven Cottage during the Reds' 1-0 defeat last week.
The 24-year-old is also facing punishment for accusations of racially abusing Manchester United defender Patrice Evra at Anfield in October.
"[Suarez] is just focusing on the game and he is happy with all the support he gets from the club, players, manager and his own fans," said Kuyt.
"This is the Premier League so [opponents] are trying to do everything to stop you and the better you are the more they try to stop you - and Luis is a really good player.
"But that is football and he knows that and he is a great professional and is just focusing on his job - that is what he does in training and in the game. Luis has done great so far and he is a great player."
Kenny Dalglish's side sit three points adrift of fourth-placed Arsenal in the Premier League table following a 1-0 win against Queens Park Rangers on Saturday.