Anorthosis Famagusta expect to agree Esmael Goncalves' transfer to Hearts in the next 24 hours.
Andreas Panteli, the Cypriot club's president, told the Evening News that he wants the deal concluded today, adding that the striker is desperate for the move to go through.
Hearts have already had two bids rejected for Goncalves, the second believed to be for £125,000. Negotiations are ongoing between the clubs for a fee of £175,000.
Goncalves played and scored for Anorthosis in their 5-0 Cypriot cup win over ASIL Lysi yesterday. After the game, he threw his shirt to supporters in an apparent farewell.
Panteli confirmed he is close to finalising the 25-year-old former St Mirren forward's transfer to Tynecastle.
"It is almost finished. We are almost there with Hearts," he said. "There are some small details, not too many things. I cannot say everything is signed but the negotiations are going on at the moment.
"It has to be done today. If it's not today, I don't have time to deal with this any other days. Today will be better for both teams.
"The player wants to go. He thinks it's a good step for his career. This is what he thinks and this is one of the points we had in mind when we started negotiations with Hearts."
Goncalves worked with Hearts head coach Ian Cathro at the Portuguese club Rio Ave. He was also coached by Cathro’s assistant, Austin MacPhee, at St Mirren.
He scored eight times in 16 appearances for the Paisley club, including in their 3-2 win against Hearts in the 2013 League Cup final.
Goncalves would become the fifth new arrival in Gorgie this month after Aaron Hughes, Lennard Sowah, Malaury Martin and Andraz Struna.