The 69-year-old Italian's position has been in doubt since Russia lost a Euro 2016 qualifier to Austria earlier this month, leaving them third in Group G and struggling to qualify for the tournament in France.
His current contract is due to end after the 2018 World Cup finals, which Russia are hosting.
Nikita Simonyan, RFU acting president, told a news conference on Wednesday: "At the moment Capello is not sacked, even though we have paid off all his debts.
"For this I would like to express my gratitude to (Russian businessman) Alisher Usmanov and (Russia`s Minister for Sport) Vitaly Mutko.
"We will conduct more talks with Capello on whether he will be working for us, or if he will be leaving us," Simonyan added.
TASS quoted RFU executive committee member Sergei Anokhin as saying: "The soap opera called 'The Capello contract' will end in the near future. I think we will agree on a contractual penalty and it will be reduced.
"We need to negotiate and reduce the amount of compensation to at least 10 million euros ($11.19 million)."
NO WINS
Capello, who coached England at the 2010 World Cup, took over as Russia coach after leaving the England job, in July 2012.
He took Russia to their first World Cup finals for 12 years in 2014 but they were knocked out in the group stage after failing to win a match.
Russia's form has not improved since, culminating in a 1-0 home defeat by group leaders Austria in their Euro 2016 qualifier on June 14. Austria have 16 points, Sweden 12 and Russia eight after six matches.
Sports Minister Mutko said last week a decision had already been made on Capello's future but gave no details.
The Italian was not paid for eight months because of the RFU's financial problems but a loan on favorable terms from wealthy businessman Usmanov helped pay his wages.
Usmanov, who has a stake in English FA Cup winners Arsenal, again bailed out Russian football's governing body on Monday to pay off the latest debts to Capello.
(Reporting by Dmitry Rogovitskiy and Vladimir Soldatkin, Editing by Timothy Heritage and Mike Collett)
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