The 25-year-old is currently on the books of Anorthosis Famagusta and netted on Wednesday in the Cypriot club’s 5-0 cup victory over ASIL.
After the match, club chairman Andreas Pantelis responded to reports linking Hearts with a move for the player, telling TV broadcasters that Anorthosis had so far knocked back two offers from the Tynecastle club.
He said: “The first proposal was last week, but the price was too low so they came back with a better proposal, but this was also not satisfactory.
“They seem to be prepared to negotiate but we haven’t come to a decision yet. We don’t know yet what they will finally decide.”
Goncalves is said to be keen on a move to the Capital and a reunion with Ian Cathro and Austin MacPhee.
Hearts assistant boss MacPhee revealed last month that his football relationship with Cathro began after the two corresponded over Goncalves’ loan deal from Rio Ave to St Mirren in 2013.
This included Cathro, who was assistant at Rio Ave, advising MacPhee to keep a very close eye on the striker, which led to a rather bizarre tale of Goncalves being brought along to the anniversary dinner MacPhee’s parents two days before St Mirren faced Celtic in the League Cup semi-final.
Goncalves opened the scoring against the Scottish champions on his debut and would score again in the League Cup final, ironically against Hearts, as St Mirren captured their first piece of major silverware in 26 years.
If the deal is successful, the Portuguese hitman will compete with Bjorn Johnsen and Conor Sammon for a place at the top of the Hearts attack.