Colombian forward Zapata was wanted by West Ham United earlier this summer before the Premier League club pulled out of a deal.
Atletico Madrid, Evian, Napoli and Sassulo have also been linked with the highly-rated Zapata, but QPR are hoping to win the chase for his signature.
QPR boss Harry Redknapp confirmed his interest in Zapata last week and the 22-year-old is now due to travel to England to undergo a medical.
Zapata's application for a work permit will have to go to an appeal and Lombardi is waiting to see the outcome of the process.
"We have approved the offer we have received from Queens Park Rangers for Duvan Zapata," Lombardi is quoted by El Dia.
"The player has permission to travel to England. There are still some details to resolve, such as the work permit and the medical.
"We haven't signed anything. From England, we haven't been informed yet if he will be given a work permit.
"Queens Park Rangers sent a better offer to us. In the beginning, it wasn't so good, but now it is and that's why we agreed to transfer Zapata to England. We only have to make better the contract that hasn't been signed yet.
"We have asked Queens Park Rangers to send us what Zapata will be doing in respect of the medical tests and his work permit. I will be travelling to Europe in the next few days."