The Reds currently top the Premier League table by two points from nearest rivals Chelsea with four games to go, with third-placed Manchester City six points worse off but with a game in hand.
Liverpool face Chelsea at Anfield a week on Saturday in a fixture that will be live on Sky Sports and could go a long way to deciding the outcome of this season's title race.
Uruguayan striker Suarez, 27, who has scored 29 league goals this season, has admitted he is avoiding media coverage of the season climax and is urging the club's supporters not to get carried away just yet.
"It's normal for the supporters to get excited and be discussing our chances," Suarez told the club's official website.
"When I'm out shopping or out with my family I bump into fans who mention it to me. I've told them to stay calm and not to worry. We'll be trying our best.
"For the players, it's probably best if we don't get involved in that kind of talk.
"Personally, I think that if I don't watch TV, listen to the radio or read about us on the internet it's better. I know what the situation is.
"Winning the title would be very special but we can't think about that yet."
Suarez paid tribute to manager Brendan Rodgers, who has done a remarkable job in his second season in charge, turning a side who finished seventh and 28 points behind league-winners Manchester United last season, into potential title winners this campaign.
"It's very important to see the manager relaxed," added Suarez.
"Brendan gives all of us confidence because he's good at his job. He believes in all of the squad and when you have that belief from your boss then it's easier to perform at your best."
You can watch Liverpool's game at Norwich on Sky Sports 1HD from 11.30am on Sunday 20 April and their home game against Chelsea on Sky Sports 1HD from 2pm on Sunday 27 April.