The striking partners have formed an impressive alliance for the Anfield club since Sturridge joined from Chelsea in January, scoring a combined tally of 12 goals in nine Premier League appearances they have made together.
Both players were once again on the score sheet as Liverpool breezed to a 3-1 home victory over Crystal Palace on Saturday, and Suarez hopes the duo can fire the Reds into the Champions League.
"We compete for the shirt of Liverpool and we try our best for the team, not for me or him," he told The Liverpool Echo. "When you have one big striker and a very good player in Daniel, I am so happy. He tries his best for the team and tries his best to play with me.
"Last season we didn't play very well and we finished in a bad position and this season we'll try to be better. If we stay with the same football style and try for the win every game, we can try for the top four."
Brendan Rodgers' charges, behind Arsenal on goals scored, continue their campaign with a trip to Newcastle United on Oct. 19 after the international break.