Despite the duo having won all but one race so far this year, the tight and twisty Marina Bay circuit will play to the strengths of Ferrari and Red Bull, which could mean a tougher time than they have had recently.
"We didn't have the greatest weekend there last year, so hopefully we're on top of that now," said Hamilton, referring to the team’s tire woes in 2015. "I guess we'll find out in a few days' time!
"Either way, it's not going to be an easy breezy drive. Even when we won there back in 2014, it wasn't straightforward.
"Ferrari and Red Bull will be on it I'm sure, so we've got a big fight on our hands if we are up at the front. I love a battle, so I'm excited to see how it plays out."
Rosberg added: "Of course, it won't be easy. This is a Red Bull track and we weren't so strong there last year. But I have faith in the team and my belief in myself is as high as ever. I approach each weekend aiming to win the race."
Mercedes is aware that no team has ever finished 1-2 at the Singapore Grand Prix, which points to the difficulties of getting the weekend spot on.
Motorsport boss Toto Wolff said: "After a strong showing in Italy, we go to Singapore with a big challenge ahead of us. No team has ever scored a 1-2 finish there - and with good reason. As we have seen before, it's a race where a single problem can cascade into many more as the weekend progresses.
"We have to optimise everything to get a solid result. We didn't manage it last year and, although we believe we now understand why, only performance on the racetrack can prove our conclusions right.
"We are curious and excited to see how it goes. Ferrari were mighty around this circuit last year and it will suit the high downforce design philosophy followed by Red Bull, so we must not make the mistake of thinking we are favorites this weekend."