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.

But Leeds chief executive Gary Hetherington has warned it could be the last played in England for some time.
Hetherington said Super League champions Leeds would have been prepared to travel to Australia.
He said: "It turned out to be too short a time scale for 2012 but it's very much on the agenda for the future."
The game will be played on Friday, 17 February.
NRL Grand Final winners Manly had proposed a Middle Eastern venue.
Hetherington told a press conference at Headingley: "Whilst there has been talk about [playing outside England] for the last eight or nine years, it's never really got far.
The fact we were prepared to play in Australia probably took the Australians by surprise
"But just recently there does seem to be an appetite, particularly from the Australian clubs, to start to explore that possibility.
"I think the fact that we were prepared to play the game in Australia probably took the Australians by surprise and it made the NRL think seriously about staging it.
"A lot of preparatory work could be done. Indeed, if it was to be in Dubai or the Emirates, work could start now for 2013."
The Rhinos have managed to secure home advantage after playing their four previous fixtures at Elland Road, home of Leeds United.
Huddersfield's Galpharm Stadium, which hosted three Challenges featuring Bradford Bulls, was considered because of its undersoil heating but Hetherington is confident Headingley can be protected against frost.
"We desperately want to win the game and if our crowd and our home stadium gives us that edge we'll certainly take it," added Hetherington.
"Whatever the weather can throw up, we'll make sure the pitch is fit. We now have a lot of technology and we won't have a game here for two weeks prior to that game."
With Headingley's capacity currently set at 20,000, the crowd will be well down on the Rhinos' previous Club Challenge matches at Elland Road. Leeds' meeting with Manly in 2009, which the Aussies won 28-20, was watched by 32,569.
Last year saw St George Illawarra beat Wigan 21-15 at the DW Stadium.

Milk will replace sugar as the treat's main ingredient, as the white stuff content is boosted from 26%  to 37.5%.
Nestle said the new recipe bars - with sugar cut by 0.7g - will be in stores by the end of the month.
It follows a similar move with its KitKat recipe, which increased the milk and cocoa content.
The Milkybar recipe has been the same since the bar first came into production in 1936, but is being changed as part of Public Health England's drive to reduce the amount of sugar consumed in the UK by 20%.
In April Nestle reduced the amount of sugar in its fruit pastilles by 30%.
A spokesman said the reductions in sugar would make "a positive step overall to removing sugar from the nation's diet while maintaining the taste"
HJK Helsinki striker Alfredo Morelos arrived in Edinburgh this morning ahead of his expected move to Rangers.
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The 2012 World Club Challenge between English champions Leeds Rhinos and Australian champions Manly Sea Eagles will be played at Headingley.
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Milkybars are about to get milkier, as the recipe changes for the first time in 81 years.