The 26-year-old arrived at Anfield from Celta Viga in June 2013 for £7.2million but appears to be on his way after just one season in the Premier League.
Aspas started just six matches for Liverpool last season and scored his only competitive goal for the team in the 2-0 victory over Oldham in the FA Cup.
Liverpool chief executive Ian Ayre has travelled to Spain to conduct negotiations with Sevilla.
During his previous spell in Spain with Celta Vigo, Aspas scored 46 goals in 136 appearances for the club.
Hindsight is a wonderful thing, but I'd rather we signed his namesake - the parrot out of Aladdin - than this fella.- ajsr1982