But the German club failed to qualify for the Champions League and were unable to make the 29-year-old's move permanent.
"He did really well in Germany last season, scoring plenty of goals, and he has told me that he wants to stay at the club and fight for his position," said Liverpool boss Rafael Benitez.
"I have told him that will be difficult with Fernando Torres and Steven Gerrard as our first-choice strikers. But he realises this and the players we have in the squad.
"But he also knows that this club always plays more than 60 games a season and that means there are opportunities. He will fight for his place. He has game intelligence, which is something we are always looking for.
"At this moment he is a Liverpool player. But it depends on him, he is continuing to work hard and is playing well so he will have a chance.
"It is good to have him back. When we signed him we were looking for a player who could play 'between the lines' as a second striker with quality."
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