Under Advocaat, Russia were eliminated from Euro 2012 after a shock 1-0 defeat to Greece in the Group stages. The RFU had indicated that Advocaat would be replaced with a star name. Manchester City boss Roberto Mancini was their potential target but on Tuesday the Italian signed a new deal which would keep him at Eastlands until 2017.
Redknapp, who left Tottenham in June despite taking them to fourth place in the table, was close to sealing the England national teams job but the FA turned to Roy Hodgson, while Capello has been a free agent since leaving the England post earlier this year.
Guardiola, who insisted on taking a year long break after deciding not to renew his contract with Barcelona, had been linked with a move to Chelsea and Russian side Anzhi Makhachkala. Capello too was linked with a move to a London based club.
Other names of the list include Rafael Benitez who last managed Inter Milan in December 2010 and Italy's World Cup-winning manager Marcello Lippi.
"The Russian Football Union has officially informed that the organisation plans to consult, in full compliance with the rules of FIFA and UEFA, the appointment of the head coach of Russian national team, with the following experts: Rafael Benitez, Anatoliy Byshovets, Marcelo Bielsa, Valery Gazzaev, Josep Guardiola, Fabio Capello, Andrei Kobelev, Yuri Krasnozhan, Marcello Lippi, Valery Nepomnyashchy, Nikolai Pisarev, Harry Redknapp, Yuri Semin," the RFU statement said.
Meanwhile, Redknapp had not been contacted by the RFU but feels the vacant post is a 'fantastic job'.
"I haven't been contacted but I'm sure it's a fantastic job for someone," Redknapp was quoted as saying in the Sun.