The 20-year-old has netted 30 goals in 43 outings for HJK - 11 of these in 12 league games - and his club are the Finnish league leaders.
Morelos moved to Finland on loan initially before sealing a £425,000 permanent transfer from Independiente Medellín in January,
It is thought that Ibrox first team coach and fellow Finn Jonatan Johansson alerted Rangers manager Pedro Caixinha to Morelos, who also scored four goals in six Europa League appearances last season.
He is a Colombian under-20 international.
HJK Helsinki are likely to want treble the fee they paid for the young striker and if Rangers can meet that valuation then Morelos could become club’s fifth summer signing after the recruitment of Bruno Alves, Ryan Jack, Dalcio and Fabio Cardoso.