The pair, who have been praised for their link-up play since Suarez returned from a 10-match ban, contributed to the Merseyside outfit's 3-1 win over Crystal Palace on Saturday.
"We compete for the shirt of Liverpool and we try our best for the team, not for me or him," the Liverpool Echo quotes Suarez as saying.
"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."
Liverpool are currently second in the Premier League table, level on points with leaders Arsenal.