The striker injured his thigh while at Newcastle before his move to Anfield in January and just returned to first-team action last month after a two-month lay-off.
"I feel I am getting towards full fitness," said Liverpool's £35 million record signing.
"I am working hard on it and I am in the gym most days doing extra work.”
The former Newcastle man revealed he was delighted to score for England in only his second game and is now desperate to get on the score-sheet for the Merseysiders.
"It was just a great feeling to score a goal again (for England) after a long injury.
"A goal for Liverpool is what I am waiting for. It's going to be great because the fans have given me a brilliant reception without scoring a goal, and now I can't wait to get a goal and make everyone happy.
The striker also said he was happy at Liverpool and has settled in well as the club since his move and is looking forward to playing regularly for Kenny Dalglish’s side.
"It's great to be here. The lads are fantastic, I get on well with all of them, and the fans are great as well.
"I'm just getting myself back to fitness now, so it's all good."