The Uruguay striker, jointly named the top flight's player of the month for March with captain Steven Gerrard, has 29 in 28 matches - having been suspended for five league games at the start of the season.
Andy Cole, in 1993-94, and Alan Shearer, in the following season, scored 34 in 40 and 42 games respectively, while the record for a 38-game Premier League campaign is 31 - achieved by Cristiano Ronaldo in 2008-09 and Shearer in 1995-96.
With five matches remaining, both targets remain within his grasp but Suarez insists team success is more important than personal milestones - and that is the reason why he has not asked to take over spot-kick duty from Gerrard.
"If I wanted to do that I could ask Stevie if I could take a penalty, but I don't like that," he said.
"For myself it is more important that Liverpool finish in a good position. I try in every game to score because I am a striker.
"I love to make goals but for me if I could swap being top scorer or winning the Golden Boot for the team finishing in the top four that would be more important.
"Of course it would be special (to break the record). In the last few years I have tried to do my job as well as I can to help the team and the Liverpool supporters.
"To finish the season as top scorer or with a new record would be nice for me, for my family and for the Liverpool supporters because it's important for them to have a player who holds the record.
"But if I think back a few games, I didn't score (he was goalless for five games in February) but I kept trying my best on the pitch."
Liverpool head into the weekend as Premier League leaders but face a crunch clash at home to title rivals Manchester City on Sunday as they look to extend their winning run to 10 successive matches.
"For some people, it's a surprise because in the Premier League it is difficult to win nine games in a row," Suarez told liverpoolfc.com.
"But if we continue at this level, we'll play very well.
"The team know we've had some really good performances in the last few weeks and we'll try to continue in this way."
"Our target was to finish in the top four and we've won our last few games.
"We also know Chelsea and City dropped some points, so we're at the top of the league now and that's amazing for us.
"Now we can't stop because we have a really good chance."
- Sports & Recreation
- Premier League
- Alan Shearer
- Steven Gerrard
- Cristiano Ronaldo