The 26-year-old Spaniard has found life in the Premier League hard going so far, having made just seven appearances under Brendan Rodgers this season.
"I want to make it at Liverpool. I'm sure the fans will see the best of me soon," Aspas told Spanish newspaper Marca.
"I knew I was coming to one of the biggest clubs in Europe to play alongside world-class players. I was always in the team at Celta and it was plain-sailing. Here at Liverpool I have to earn my place, just like any other signing.
"It's not easy breaking into a team with so many top-class players. It's not easy breaking into a team with so many top-class players. I'm working hard every day to try to get more game time."
The midfielder's lack of starts this season has pricked the ears of a number of clubs, including both Valencia and Real Betis who are said to be interested in the player.