The 26-year-old has had a string of injury problems since moving to Anfield from Chelsea in 2013.
After spending most of the first half of the current campaign on the treatment table, Sturridge has worked his way back to fitness but is struggling to hold down a starting spot under manager Jurgen Klopp.
Divock Origi was first-choice striker, but after he was struck down by an ankle injury, it was widely expected that Sturridge would resume his role up front.
However, the England international was left on the bench during Thursday's 1-0 defeat to Villarreal in their Europa League semi-final first leg, and Christian Benteke was chosen to come on as a late substitute instead.
"There are things I want to achieve with Liverpool, [but] I would never say I am Liverpool until I die, because I would be lying," Sturridge told The Mirror.
"I think any player who says, 'Oh yeah, this is the only team I will play for, for the rest of my life', they are deluded. In football, every team looks for replacements every single year.
"So for myself all I can do every weekend is go out there, perform as well as I can, perform to the best of my abilities, and then come the end of the season hopefully have the European Championship to look forward to, and to next year."
Sturridge has scored in his last four Premier League games.