But the Uruguayan forward is delighted to hear fans chanting his name early on in his career at Anfield, having joined the club only in January, and understands the role they play
The Uruguay international arrived in the January transfer window after a fee reported to be in the region of £23 million had been agreed with Ajax.
After Fernando Torres's departure to Chelsea, the 24-year-old's performances have seen him become an instant fan favourite at Anfield.
However, the forward insists that he needs to offer a lot more than he already has to go down as a truly great player in the history of the club.
"It’s great the fans are singing my name, but there is a lot of time to go before I am a real hero – it’s too early for that," said Suarez, according to The Mirror.
"The fans here play a major role. I might not understand what exactly they are singing, but I know it’s my name. That’s important to me. It’s good to see they are happy."
Suarez has scored two goals and has two assists to his name in five Premier League appearances.