After returning from a profitable loan spell with Bundesliga outfit Hertha Berlin in the summer, the Ukraine striker has yet to find the back of the net in eight appearances for the Reds this term.
However, Voronin admits he holds a strong desire to prove his worth at Anfield, and is eager to give fans something to cheer about in the coming weeks.
"Last season was good for me because I wanted to play more matches," the 30-year-old told Liverpoolfc.tv.
"I went to Hertha Berlin, played a lot of games and scored goals. I was happy there.
"But I always wanted to come back to Liverpool because they are a massive club.
"It is very important for me to be here. I've spoken with Rafa and I want to take my chance, work hard and play for Liverpool."
He added: "I hope in the next game I play, I can give the Liverpool supporters more."
Voronin watched from the stands as Liverpool were held to a frustrating 2-2 draw by Birmingham City at Anfield on Monday evening.
The result means the Reds have won only once in their last nine matches in all competitions - a statistic the No.10 acknowledges to be disappointing.
But Voronin insists there is a steely resolve amongst the squad to reignite their campaign and cites last month's victory over Manchester United as proof of what Liverpool are capable of.
"The season hasn't started well for us," he said. "We have dropped a lot of points, but the season is long.
"We can play better, everybody knows that. We played really well against Manchester United last month and showed a lot of good determination.
"There is a strong desire amongst the players to turn things around. We want to try and win every game and we will do our best both in training and matches."
Liverpool are currently in the midst of a two-week hiatus from action due to the international schedule.
Though with several first-team players sustaining injuries in recent weeks, Voronin is hoping the recess will allow the squad time to recover ahead of the Reds' next outing against Manchester City on November 21.
He said: "The break could have come at a good time for us because we have a lot of injured players who cannot play.
"I think it is a good time for us to take a break and prepare for the next game."