Las Palmas president Miguel Angel Ramirez says Jese Rodriguez wants to join the club despite more lucrative offers from elsewhere.
The Paris Saint-Germain forward has long been linked with a return to LaLiga with his boyhood team, although Ramirez has always maintained they cannot offer the same financial incentives as other interested parties.
Middlesbrough boss Aitor Karanka confirmed on Thursday he was hoping to convince Jese to sign from PSG, while Roma have also been linked.
But Ramirez claims Las Palmas have never been closer to completing what would be a major coup, telling Cadena SER: "Fortunately, I'm seeing Jese closer to Las Palmas.
"We can't compete financially with the others who want Jese but the player himself wants to join.
"[Friday] will be a key day in the negotiations. We've never been so close to signing Jese."
The arrival of the former Real Madrid man would complete a strong week in the transfer market for Las Palmas, who announced the signing of Alen Halilovic from Hamburg on an 18-month loan deal on Thursday.