The Frenchman, 60, quit on May 9 after failing to overturn his ban from all football activities, BBC reported.
Platini was found guilty of ethics breaches over a 2-milliom-Swiss franc (£1.3m) payment he received from FIFA.
The former France captain and three-time Ballon d'Or winner was initially banned for six years but had the punishment cut to four years.
UEFA interim secretary general Theodore Theodoridis said the 55 national federations would vote at an extraordinary congress in Athens, Greece.
The new president will complete Platini's term, which runs through March 2019, and become a FIFA vice president.
Possible replacements include Slovenian federation president Aleksander Ceferin and UEFA vice-presidents Angel Maria Villar and Michael van Praag.
The deadline for contenders to register is July 20.