The post became vacant after Dick Advocaat stepped down in the wake of Russia's humiliating Euro 2012 group stage exit.
The names published on the Russian Football Union website are: former Inter and Liverpool manager Rafael Benitez; Athletic Bilbao coach Marcelo Bielsa; former Russia coach Valery Gazzaev; former Barcelona coach Guardiola; former England boss Capello; former Dynamo Moscow coach Andrei Kobelev; former Anzhi Makhachkala coach Yuri Krasnozhan; former Italy coach Marcello Lippi; former Cameroon coach Valery Nepomnyashchy; under-21 coach Nikolai Pisarev; former Tottenham Hotspur coach Harry Redknapp and Dynamo Kiev coach Yury Syomin.
Russia's sports minister Vitaly Mutko vowed last week to settle on a coach by July 21.
Five of the 13 - Guardiola, Capello, Redknapp, Benitez, and Nepomnyashchy - are currently free agents.
Guardiola, 41, stepped down as Barcelona coach in June after winning 14 titles in four years at the Camp Nou.
Sixty-six-year-old Capello resigned from the England job in February in protest at the English FA stripping John Terry of the captaincy.
Redknapp, 65, left Spurs last month after losing out on the England post to Roy Hodgson and subsequent talks on a new contract at White Hart Lane collapsed.
Benitez has been out of work since December 2010, when he was fired by Inter Milan after a string of poor results.
Of the other foreign candidates, Bielsa, considered one of Europe's most innovative coaches, recently indicated he would stay with Bilbao, where his contract expires in
Lippi, 64, won the 2006 World Cup with Italy and ended his second stint with the national side in 2010. He started coaching again this year in China, taking over at Super League side Guangzhou Evergrande in May.
Of the Russian options, meanwhile, Gazzaev might be seen as the strongest candidate.
The 57-year-old took CSKA Moscow to the UEFA Cup in 2005, the first European silverware won by any Russian team, and took four Russian league titles.