Health officials in American Samoa have been discussing how to restrict non-immunised travellers from Samoa entering the territory.
They may be asked to show proof of immunisation before they are granted entry.
This follows two suspected measles cases being admitted to the LBJ Hospital on Sunday.
The two are children under five from Samoa who arrived on the Lady Naomi on 31 October.
Neither had been immunised against measles.
Meanwhile epidemiologist Aifili Dr John Tufa is advising parents in American Samoa to look out for acute fever, cough, conjunctivitis and headache, after which a rash can start.
"This rash is very specific," Dr Tufa said.
"It usually starts off from the head, so right below the hairline, behind the ears and the neck and then slowly spreads down to the torso and eventually covering the entire body."