The Dutchman is a popular figure at Anfield and finished last season as Liverpool's top scorer but the arrivals of Stewart Downing and Jordan Henderson have raised concerns about his ability to secure a regular starting place in the coming season.
But Kuyt is confident that the fight for starting spots can only be a good thing for Liverpool's chances of success.
"I am very happy with the signings we have made this summer and it was good for them to have their first game at Anfield," Kuyt told the club's official website after Liverpool's 2-0 friendly victory over Valencia on Saturday.
"Everyone wants to play, but rivalry is something that in my opinion belongs to a club such as Liverpool. That's what should happen, you have to double up in every position.
"We want to progress and move forward and to do that you need more than 11 good players."