"In accordance with Russian law, citizens of Russia cannot be turned over to foreign states," the agency quoted prosecutor's office spokeswoman Marina Gridneva as saying.
The office could not immediately be reached by The Associated Press for confirmation.
However, a Russian lawmaker raised doubts about the reported claim that Russian law prevented such extraditions.
Yuri Sharandin, chairman of the constitutional legislation committee of the Federation Council, the upper house of parliament, said it was possible for Russia to extradite its citizens, but that it also could refuse such requests.
Sharandin said on Ekho Moskvy radio that the matter would come under the European Convention on Extradition, to which both Russia and Britain are signatories.
He said the convention allows for such extraditions, but also gives the country receiving the request the right to refuse.
Turkey has found itself in a circle of countries subject to US and European sanctions. Are they dangerous for Ankara? What is Turkey going to do in response?