Several people have reportedly seen the whales, a rare sight in the area, off the coast between the popular tourist towns of Newquay and Padstow over the last 10 days.
Ocean scientist Dom Clarke, 25, saw what he believes was a mother and calf near Trevose Head, five miles from Padstow while walking along the cliff.
He said he saw them heading south towards Newquay, which is around 10 miles away and home to a colony of grey seals, a popular food source for the whales.
He told how he came across a man with binoculars who asked him what species of whale he thought they were.
"I thought 'wow, that is pretty unusual to see', so I grabbed the binoculars," he said. "At the time they were heading south along the coast about 100 metres off the headland. It was pretty special."
Killer whales (Orcinus orca), also known as orcas, can grow up to 32 feet in length and weigh up to nine tonnes. The distinctive triangular dorsal fin can grow up to six feet high.
They are mainly found around Iceland, Norway and northern Scotland, but occasionally some are seen as far south as the Atlantic coasts of Spain and Portugal and east into the Mediterranean.
According to the SeaWatch Foundation, killer whale sightings are rare in the waters off the coast of South West England, with most sightings between March and September.
Angie Gall, marine conservation officer with the Cornwall Wildlife Trust, said that it is thought the whales merely pass through the area en route to more northerly waters around Scotland.