The RIA news agency cited the FSB as saying that the hijacked jet was to be flown toward a NATO air base in the Romanian city of Constanta, where it could have been shot down by air defences, the agency reported.
The FSB, the main successor to the Soviet-era KGB, said Ukraine and Britain had planned a large-scale "provocation" using the hijacked aircraft, and that Ukrainian military intelligence had sought to recruit Russian pilots for $US3 million ($A4.6 million) to steal the fighter.
"The measures taken have thwarted the Ukrainian and British intelligence services' plans for a large-scale provocation," RIA cited the FSB as saying.
State TV showed pictures of messages and recordings of a man who they said was working for Ukrainian and British intelligence and had offered millions of dollars to a Russian pilot to fly a MiG to Europe and that the pilot had also been offered citizenship.
Reuters could not independently verify the account.
Russia's Kinzhal is an air-launched ballistic missile that Moscow calls hypersonic, capable of very high speeds and manoeuvring flight paths intended to make it difficult for air defences to track and intercept.
Russia has long cast Britain as its main enemy. Moscow accuses London of stoking the Ukraine war and British intelligence of helping Ukraine to mount a series of operations deep inside Russia.
Britain casts the Russian invasion of Ukraine as an imperial-style landgrab by Moscow. London has repeatedly warned that Russian intelligence is trying to sow mayhem across Britain and Europe to undermine democracy.
