Zenden has done pretty well in the the Reds' pre-season games so far but has promised Liverpool fans that there is more and better to come.
He said: "As a team, I think we have been improving with each game but looking at my own form I would say there is much more to come from me in the coming season. I've been fairly pleased with how things have gone but with the hectic schedule of games it hasn't been easy.
"Also, the tempo is never as high during pre-season and it's only when the serious games begin that players really begin to find their true form. I've been disappointed not to have got on the scoresheet but I'm determined to put that right as soon as possible.
"I haven't set myself any particular goalscoring targets and I suppose it doesn't really matter who scores the goals so long as the team is winning but I'd love to be more prolific in front of goal once the season starts. You can't just rely on the strikers to score, I'm well aware of that and my aim is to chip in with a fair share of goals myself."