It is not clear when the fleet will sail past Portugal.
The carrier is expected to be flanked by dozens of Russian warships and a number of submarines as it sails past the Portuguese coastline en route to Syria.
Nato recently accused Russia of provocative military manoeuvres, especially in the Baltic region as Russian warplanes stepped up patrols near Nato countries’ airspace.
The British Ministry of Defence said on Thursday that the British destroyer, HMS Dragon, was due to meet two Russian corvettes travelling north towards the UK from the direction of Portugal.
The Admiral Kuznetsov can carry more than 50 aircraft and its weapons systems include Granit anti-ship cruise missiles.
The other Russian surface ships in the group are the nuclear-powered battle cruiser Peter the Great, two large anti-submarine warships - the Severomorsk and Vice-Admiral Kulakov - and four support vessels.
BBC reported Russian armed forces channel TV Zvezda as saying several submarines would probably move from the Atlantic to escort the flotilla.