The Uruguayan striker, whose 29 league goals have underpinned Liverpool's challenge, admitted he cannot bring himself to follow the climax to the season through the media.
"It's normal for the supporters to get excited and be discussing our chances," Suarez told the club's 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 Brendan Rogers, who will be favourite to take the manager of the year title if Liverpool - currently two points clear of second-placed Chelsea - can win their remaining four matches, starting at Norwich City on Sunday.
"It's very important to see the manager relaxed," Suarez said.
"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."
Suarez's strike partner, Daniel Sturridge, is available for the trip to Carrow Road but is far from certain to make the starting line-up.
The England international limped out of Liverpool's 3-2 victory over Manchester City last weekend with a suspected hamstring injury, and the club confirmed on Wednesday that a scan had revealed a "small strain".
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- Brendan Rogers