Zamalek's statement comes a few hours after arch-rivals Ahli announced they were pulling out of the race to sign the Egypt international.
Zamalek president Mortada Mansour announced the deal in a press conference in the club headquarters on Wednesday.
The conference was attended by Lokomotiv's Tunisian agent Radhi Al-Dreidi and Zamalek board member Khaled Latif.
Mansour told the press that the Cairo club has finalized a deal with the Russian giants that will allow Zaki to complete the move.
Mansour, however, refused to disclose the financial details, noting that these details could affect Zamalek's players who still have to compete in the Egyptian Cup.
But inside sources claim Zaki will ink a contract that will see him earning EGP 5 million over three years.
Lokomotiv's cut of the deal is reportedly 1.4 million Euros (approximately EGP 10.4 million).
The 23-year-old Zaki is currently in Germany receiving treatment for a knee injury he had previously picked up.
The former Enppi goal-getter did not feature once for Lokomotiv since joining them in March.
Zaki was a pivotal member of the Egyptian team that won the African Cup of Nations on home soil last February.
Meanwhile, Al-Dreidi refused to comment on the reasons behind Ahli withdrawing their bid for the player.
Ahli marketing director Adli Al-Qaeyi had claimed the club was not interested in signing Zaki anymore due to the high price tag set for the player.