Sports Minister Mutko announced on Tuesday he would step down next week as president of the football federation (RFU).
He was forced to resign after Russia President Dmitry Medvedev decided last month that all government officials in charge of national sports bodies should be replaced by professional personnel.
A member of parliament since 2003, Kapkov heads the Abramovich-sponsored National Academy Fund (NAF) which supplies most of the RFU's money.
"Sergei has significant support within political and business circles as well as among the soccer community," NAF vice-president Alexander Edelstein told Reuters.
"Since its inception in 2004, NAF has spent well over $200 million on various soccer projects such as building pitches and running youth academies in many parts of the country."
Earlier this month Kapkov was quoted as telling Russian media: "I plan to run for president of the RFU".
Kapkov was elected RFU vice-president in April 2006 at the age of 30.
HIDDINK SUPPORT
Russia coach Guus Hiddink said he would welcome Kapkov's appointment.
"I would support him," the Dutchman told Reuters on Monday before departing for Maribor where his team will defend a 2-1 first-leg lead in Wednesday's World Cup playoff return against Slovenia.
"It would make my job as Russia coach much easier," said Hiddink who has often criticised RFU bureaucracy.
Hiddink, whose salary is largely paid by billionaire Abramovich and who had a brief spell in charge of Chelsea last season, said Kapkov's appointment would increase the chances of him extending his contract.
"It would certainly make my dialogue with the RFU a lot easier," said the Dutchman whose existing deal will expire when Russia's involvement in the World Cup ends.
The new football chief will be elected by the RFU's general assembly in February.
