The 21-year-old impressed during a five-month stay at Tynecastle last season and is all set to return for a second spell on loan.
“We’re nearly over the line with Demy,” said Levein after the 1-0 victory over Kilmarnock on Saturday afternoon. “I don’t want to go into the details, but it would be another loan deal.
“We need a striker, we need a left-sided player and we need a centre-back.”
Another player who could return to the club is Osman Sow. The Swede is believed to have failed a medical, though Hearts insist the deal for the MK Dons striker is not yet dead.
Asked about the situation, Levein said: “I don’t know what’s going to happen there, but it’s still in the melting pot, so to speak.”