The Straits Times understands the undelivered items, which are mostly watches, are worth at least $32m.
In response to ST’s queries, a police spokesman said the reports were made against two companies, Tradenation and Tradeluxury.
He added: “The complainants alleged that they made advance payments for luxury watches or luxury bags to the companies, which failed to deliver them.”
The police arrested a 26-year-old Singaporean man on June 27 for his suspected involvement in cheating offences.
His passport was impounded and he was released on bail the next day, pending the completion of investigations, said the police.
His wife, 27, was also assisting the police with investigations and surrendered her passport to the police on June 30. The couple subsequently became uncontactable.
ST understands the woman is a Thai national.
The police said they arrested a 40-year-old Malaysian man last Wednesday who had allegedly helped the couple in leaving Singapore on July 4.
The man was charged last Friday with abetting another person to depart Singapore illegally.
The police spokesman added: “The police are working closely with foreign law enforcement counterparts to trace the couple and the criminal proceeds.
“Warrants of arrest and Interpol red notices have been issued against the couple.”
Those convicted of cheating can be jailed for up to 10 years.
The Ministry of Law had told ST on Tuesday morning that Tradenation was registered as a precious stones and precious metals dealer on April 2.