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Mutko is head of the Russia 2018 organising committee but his involvement in the World Cup was thrown into doubt on Tuesday when he was banned from the Olympic Games for life by the IOC due to his implication in a state-sponsored doping scandal.
But Sorokin insisted that decision had no impact on the World Cup.
"It has no connection to football. Mr Mutko is chairman of the local organising committee," Sorokin told AFP from the UEFA executive committee meeting in Nyon, Switzerland.
"Our goal remains the same, that is to deliver the most successful World Cup in history.
"(World football governing body) FIFA was exhaustive on that matter: there is no connection to football, we keep on doing what we have been doing for six years now."
FIFA had stated on Tuesday after the IOC's announcement that former Russian Sports Minister Mutko's ban had no impact on the World Cup.
Sorokin also dismissed accusations in the explosive World Anti-Doping Agency-sponsored McLaren report that Russian footballers had been part of the state-sponsored doping programme.
FIFA has contacted Canadian law professor and sports lawyer Richard McLaren about his report, in which he listed a number of Russian footballers.
"Our team players have been tested on multiple occasions, at every competition that they took part: Euros in France, (the World Cup) in Brazil, in their club competitions," said Sorokin.
"Every time they were tested there has not been a single positive result, so we are clean."
As well as being deputy prime minister, Mutko is president of the Russian football federation and has close ties to Russian President Vladimir Putin.
In fact, even after the damaging allegations emerged, Putin promoted Mutko from Sports Minister to Deputy Prime Minister, while several subordinates to Mutko were either fired or resigned.
