The 25-year old Spain player is expected to arrive in England for his medical next week after the La Liga season ends this weekend.
Celta Vigo are playing Espanyol and must win to stand a chance at staying in the top flight with Aspas needed to try and change their future.
It is believed the former Swansea City target will join the club for around £9million after a fairly successful season where he scored 12 goals and made 5 assists.