Sergei Stepashin suggested that the funds to honour the Italian's contract were not in place, though he is hopeful a resolution can be found by Saturday, when Russia face Austria in a Euro 2016 qualifier.
"I declare that money to pay salaries [to] Capello at the RFU is not there," Stepashin, who described the situation as "extremely unpleasant", told Interfax.
"It's wrong, but when they signed the contract they should have thought through how it's going to be financed. Today we need to look for sources of funding."
It has been reported that the former England boss has not been paid since June, with his patience thought to be running out.
Russia, who failed to qualify from their group in the World Cup, agreed a contract extension with Capello in January to take the 68-year-old through to the 2018 World Cup.
He has led them to a return of five points from three qualifying matches for Euro 2016.
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