"I think Capello has all the necessary requirements to coach the Russian national team, (but) personally I would prefer Mourinho," Mutko told Russian state television Rossia 2 on Wednesday.
The charismatic Mourinho is one of the most sought after coaches in world soccer but with the Portuguese committed to staying with Real Madrid, former Russian FA (RFU) chief Mutko hopes Capello will sign a contract within the next two days.
"Today or tomorrow we should iron out all the details so a contract could be signed before the start of the Russian Premier League (on Friday)," said Mutko.
Capello, who quit as England manager in February, is set to succeed Dutchman Dick Advocaat, whose contract expired after Russia failed to get past the group phase at Euro 2012.
Russian media reported that the 66-year-old Italian, who has had success coaching top clubs such as Real Madrid, AC Milan, AS Roma and Juventus, would earn up to 10 million euros a year after signing a contract through to the 2014 World Cup, with the possibility of extending it for another two years.