The 26-year-old forward was snapped up from Celta Vigo in 2013 with the intention of being another creative link in the final third of the field.
Brendan Rodgers splashed out over £7million on the Spaniard, but has seen little return on that investment.
Aspas has struggled for form and fitness, restricting him to just 12 appearances in all competitions - in which he has netted only one goal against Oldham Athletic in the FA Cup.
He admits that he has found the going tough, and that his situation is unlikely to improve as he competes with talismanic figures such as Luis Suarez, Daniel Sturridge and Philippe Coutinho for first team recognition.
As he is at an age where a short-term loan spell would offer little benefit, Aspas has now conceded that it may be in the best interests of all concerned if he cuts short his English adventure at the end of the season.
He told FTBpro: "I'm not 20 years old anymore, I can't go on loan and explode.
"I think the best would be to transfer to another club that I find the best fit for myself and the club."
On his lack of game time on Merseyside, Aspas added: "This is the hardest part. I used to play almost all the matches and I arrived here playing much less. This is the tough side of football."