The 25-year-old has scored 12 times in La Liga this season and with Luis Suarez missing the start of the season due to his ban for biting Branislav Ivanovic, Brendan Rodgers has moved swiftly to sign another striker.
Aspas will play in his side's final league encounter to help them try to avoid relegation before flying to Liverpool next week to discuss personal terms and undergo a medical.
The striker is no stranger to controversy though. He recently received a four game ban for head-butting Carlos Marchena of Deportivo.
Aspas has spent his whole career at Celta and made his debut in 2008. He was the club's top-scorer with 23 league goals last season as they were promoted back to the Spanish top flight.
Celta are one point adrift of safety heading into Saturday's clash at home to Espanyol with 17th placed Deportivo hosting Real Sociedad.
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