The 29-year-old has played his part this season with four goals in all competitions, including two in the Premier League despite the fact he has managed just two starts - with nine further appearances from the bench.
There have been reports of MLS interest in Sturridge and West Ham have also been mooted as potential suitors, but the former Manchester City and Chelsea striker says he isn't thinking about his own future as Liverpool seek to end their long wait for the top domestic prize.
"I'm staying focused on right now. You've got to live in the present, you can never live in the future. I've been at Liverpool for a long time and I'm happy too," he told BBC Radio 1Extra.
"I want to try and help bring the team some success, to win a trophy with them would be amazing. We've come close before, finals, almost won the Premier League before but we didn't quite do it."