The veteran Italian coach, who led England at the 2010 World Cup and then took over Russia two years later, has not been paid since June.
And since that time, the national team has won only one of six competitive matches.
Russian Sports Minister Vitaly Mutko, who played a crucial role in attracting Capello in 2012, seems to think the team's struggles and the coach's missing paychecks are related.
"(It) doesn't give either the team or the coach any extra motivation," Mutko said of the lack of pay, adding that the ordeal "could be having an effect on the team's results."
Capello, however, has denied that either he or the team is distracted by the dispute.
The reason for the monetary snub is not clear, but the Russian Football Union has repeatedly struggled with financial problems. RFU president Nikolai Tolstykh has even said the organization was forced to take out bank loans in recent months to pay some members of Capello's staff.
Russia's poor showing at the World Cup in Brazil, when the team was eliminated in the group stage, prompted some lawmakers to criticize Capello's reported $11 million yearly salary.
Nationalist politician Vladimir Zhirinovsky branded Capello "a thief," while Igor Ananskikh, head of the sports committee, said Russia's team was the weakest in a decade and ordered the coach to testify before parliament. Capello has yet to do so, but the call was repeated this week after Sunday's 1-1 draw with Moldova.
Qualifying for the European Championship started with a 4-0 win over Liechtenstein, but that was followed by draws with Sweden and Moldova. The latter result dampened celebrations of Russia's first match at a completed stadium for the 2018 World Cup, Spartak Moscow's new Otkrytie Arena.
At a time when Russia is eager to present itself as a global sporting giant, hosting the Winter Olympics in Sochi and preparing for the next World Cup, failing to pay its highest-profile foreign coach jars with that image.
"This whole situation doesn't make Russia look good in any way," Mutko told local media.
Mutko was head of the RFU for four years until 2009, the year after he became sports minister, and remains a major figure in football as Russia's representative on the FIFA executive committee. Reports have linked Mutko with a possible return to the helm of the RFU as president, but he has not commented on the rumours.