Pending a successful medical, the 20-year-old Colombian would become the sixth signing of the summer at Ibrox.
Morelos spent 16 months in Finland, after arriving from Independiente Medellin, and scored 47 goals in 62 appearances for HJK.
The forward, who has six Under-20 caps, would require a work permit to play in the UK.
Morelos would join Bruno Alves, Ryan Jack, Dalcio, Fabio Cardoso and Daniel Candeias as new arrivals at Ibrox, as manager Pedro Caixinha looks to overhaul his squad in time for the Europa League qualifiers, which begin on 29 June.
HJK Helsinki striker Alfredo Morelos arrived in Edinburgh this morning ahead of his expected move to Rangers.