The Asian tiger mosquito is one of the vectors responsible for transmitting dengue fever. Photo: SCIENCE PHOTO LIBRARY
Case numbers have been decreasing since 1 May.
In the lastest update (13-19 May), the Ministry of Health said there were 18 cases, down from 62 recorded the previous week.
"If this trend continues then Friday next week we will be calling the outbreak off," Aiono said.
"Dengue is actually endemic in the country, so you expect of course just a small number."
He said the outbreak was called when case numbers consistently surpassed 10 a week and he would like cases to dip below that number before calling it off.
There have been no deaths from the outbreak.
The Ministry of Health declared the dengue outbreak on 19 April.
Since then, the public have been advised to remove stagnant water sources - which mosquitos use as breeding sites - wear clothing that minimises mosquito bites and use repellents.
Hospital, schools and other public places have also been fumigated over the past four weeks in response.
Aiono said he was very pleased with the "multi-sectoral approach" that involved all government ministries including Samoa Tourism Authority.
Meanwhile, influenza cases have been high, surpassing normal seasonal increases but below the alert threshold.
From 13-19 May, there were 991 cases of influenza were recorded according to Ministry of Health data.
Aiono said some of the cases are likely come from New Zealand and Australia.
He said some people with influenza have progressed to have more serious respiratory illnesses like pneumonia.
"It is a concern and we have imported the flu vaccines hopefully we can vaccinate all those who are high risk of getting the flu and developing complications."
Aiono said everyone who comes to hospital is now required to wear a mask.
Two people died from a dengue outbreak in 2017.