Israeli newspaper Maariv said the embassy will initially move to a 13-storey structure, with underground parking and a hotel.
An embassy spokesman said that a leasing deal had been concluded, but that plans to construct a new building were being considered.
A spokesperson for the multi-millionaire, rumored to have amassed vast wealth from arms deals with Angola, did not give details on proposed construction deal, but said commercial interest was "not the priority".
"If it was simply a residential building being built, then this would probably be more profitable," he said.
Gaidamak and Roman Abramovich, governor of the Chukotka Region and owner of London's Chelsea FC, were earlier reported to have accepted the Russian government's request that they provide funds to repossess Orthodox Church buildings in Jerusalem that Israel bought from Soviet authorities 40 years ago.
The two buildings - St. Sergius' church and the Ecclesiastical Mission - are part of Jerusalem's so-called Russian Compound. The churches were built in the final decades of Tsarist rule and partially sold to Israel by the Soviet authorities in 1964. Israel paid for the assets with a shipment of citrus fruit in what went down in history as the "orange deal".