The towering defender is seeking to find a new club after terminating his contract with Zamalek by mutual consent.
Masri revealed last week that they were interested in signing him and now Ittihad also said they were tracking him.
"We opened talks with Azmi over a possible transfer," Ittihad coach Taha Basri told FilGoal.com on Sunday.
Ittihad, who heavily improved under Basri after struggling at the wrong end of the table for several years, are also close to signing free agent Mohamed Abdullah.
The versatile midfielder was released by Zamalek following the end of last season after failing to prove his worth during a year-and-a-half spell at the Cairo giants.
"If we sign Azmi and Abdullah, we will end our activities in the summer transfer window," Basri added.
Ittihad signed a host of players in the close season, including veteran defender Shadi Mohamed from Ahli and Zamalek duo Mohamed Al-Morsi and Mohamed Ibrahim.