Russia are giving coach Leonid Slutsky time to change his mind before they accept his offer to resign.
Slutsky said the 2018 World Cup host nation would be better with a new coach after they exited in the group stage of Euro 2016 with defeats to Slovakia and Wales.
Russian Football Union head Vitaly Mutko, who is also the country's sports minister, suggests he wants Slutsky to change his mind.
Mutko told Russian media: "Let's give him a bit more time, everyone's still emotional,'' but admits Slutsky could still leave.
Slutsky, who splits his time with CSKA Moscow, took over as Russia coach last year and rescued a Euro 2016 qualifying campaign which had been in trouble under his predecessor, Fabio Capello.
On Tuesday, AS reported that departing Manchester City boss Manuel Pellegrini had been offered the job.