The 23-year-old moved to Paris Saint Germain in the summer but has failed to establish himself in the French captial.
And his hopes of minutes were hit by the arrival of Julian Draxler earlier this month.
But the former Real Madrid winger, who have been linked with Liverpool and Middlesbrough, is now on the verge of return to Spain to revive his career.
"The Jese procedure is practically finished, there's a complete agreement," Ramirez told UD Radio.
Jese Rodriguez is on his way back to Spain
"The intention is to present him tomorrow [Tuesday] in the Estadio Gran Canaria in front of all the fans. We need the best number of fans possible at the presentation.
"Jese is losing a huge amount of money but he wanted to defend the colours of Las Palmas.
"We can't go more into the deal than we have. Ultimately, our objective was to get Jese and that's been possible."