Three of the naval vessels are expected to make a stop at Gibraltar, The Daily Telegraph reported.
The navy insisted the vessels' four-month deployment in the region was part of a military exercise that had been planned for several months.
It comes as Spain is threatening to tighten rules on visitors to the British territory of Gibraltar.
The Response Force Task Group, comprised of nine vessels, is scheduled to depart England Monday.
The group, led by the helicopter carrier HMS Illustrious, will sail through the Mediterranean and on the Persian Gulf and the Horn of Africa.