The play written by Lucy Prebble is based on the book dubbed A Very Expensive Poison by journalist Luke Harding, the Guardian reported.
The theater is expected to officially announce the premiere next week.
Litvinenko has moved to the United Kingdom in 2000. Six years later he was naturalized, however, the very same year, he began to feel ill. Litvinenko died in late November 2006, with UK doctors explaining his death by radiation poisoning.
The investigation, however, failed to prove that the polonium-210, allegedly used to poison the former intelligence officer came from Russia.
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The Russian Foreign Ministry refuted allegations about Litvinenko's murder and criticized the UK inquiry as politicized and lacking transparency, saying that it would have an adverse effect on relations between the two nations.