The Uruguayan has scored 11 times just four appearances against Sunday's opponents, including four in the reverse fixture at Anfield in December, which Liverpool won 5-1.
If Suarez scores a hat trick at Carrow Road for the third season in succession, he will break the Premier League record of 31 goals in a 38-game season, held by Alan Shearer (1995-96) and Cristiano Ronaldo (2007-08).
Jordan Henderson is definitely out, serving the first of a three-match suspension after receiving a straight red card in the 3-2 win over Manchester City last weekend.
"We never look too far ahead and that's the key to managing that expectation," said manager Brendan Rodgers. "We have to do the job against Norwich. We've had other games where we've had pressure, we had to stand up and be counted. We do not underestimate them, we know they are a threat."
Rodgers will be wary of a Norwich side fighting for its life at the wrong end of the table, and manager Neil Adams will hope to hit the ground running in his first home game in charge since the departure of Chris Hughton.
A 1-0 defeat at Fulham last time out leaves Norwich just one place and two points clear of the bottom three.
Despite the disappointing result, Adams saw positive signs in defeat, and sees no reason why Norwich cannot bring to an end Liverpool's blistering run of form.
"I saw everything I wanted to see apart from a goal," he told the club's official website. "They're the best team in the country at the moment on merit, they're top of the table and it's their title so to speak, it's theirs to lose.
"It's been such a long wait so it brings its own pressure. All runs are due to come to an end sometime and why not at Carrow Road on Sunday?"
Adams also confirmed that long-term absentee Elliott Bennett (knee) remains out, as does Joseph Yobo (calf).