The move has been in the pipeline for some time and will be confirmed when the necessary paperwork is completed.
Aspas scored 12 goals in 34 games this season for the La Liga strugglers, whose place in the Spanish top flight was only confirmed on the final day of the campaign.
The 25-year-old was directly involved in 51 per cent of his team's goals this season having broken into the senior side in 2009 after coming through their youth set-up.
Aspas can play through the middle or on the wing and would become Liverpool manager Brendan Rodgers' second signing of the summer transfer window if the deal goes through.
Centre-back Kolo Toure agreed a move to Anfield from Manchester City in late May and it will be completed at the beginning of July.
Rodgers' summer strengthening is beginning to gather pace as Liverpool are also hopeful a deal can be done for Sevilla youngster Luis Alberto.
The 20-year-old has been on loan at Barcelona B but yesterday was the deadline for the Catalan club to offer the midfielder a permanent contract.
Having tracked the youngster's progress and made it clear to his parent club they are interested in a deal Liverpool are optimistic they can add the promising talent to their ranks.
Rodgers is keen to get as much of his business done as quickly as possible and they have reportedly made a move to bring in Sporting Lisbon's 20-year-old defender Tiago Ilori while attempts are being made to secure the services of Schalke centre-back Kyriakos Papadopoulos.
Liverpool have also been linked with Sunderland goalkeeper Simon Mignolet.
The club hope to offset some of their outlay by selling striker Andy Carroll to West Ham but although a £15million-plus deal has been in place for some time, the player is stalling on agreeing to the move.