A report in the Dutch online site Volkskrant said telecommunications experts had opined that the only way this could have happened was by the British spy agency GCHQ tapping the information and then handing it over to Appen.
Both Appen and GCHQ have been contacted for comment.
According to Volkskrant, the matter came to light through a Dutch woman who had been employed by Appen in the UK. The company has four main offices: in Sydney, Seattle, San Rafael (California) and Davao City (the Philippines).
This woman was tasked with describing thousands of short audio excerpts in which she heard Dutch people chatting on the phone, with many of them being communications by cabbies in The Hague.
In one excerpt, she recognised the voice of an ex-boyfriend, who was speaking via Vodafone. He had not given the telco permission to share his calls with anyone and confirmed this to Volkskrant.
The woman was able to confirm her employment with Appen to the website.
Volkskrant spoke to two senior employees of big telcos with knowledge of the rules around tapping telephone conversations; they told the website that conversations and data of their clients could be provided to third parties only by law enforcement or state spy organisations.
The website quoted Rene Pluijmers, a telecommunications expert with the Dutch National Forensic Investigation Bureau, as saying he suspected the hand of an intelligence agency behind the leak.
"The British agency GCHQ is tapping dozens of fibre optics cables, also cables coming from the Netherlands, and they have experience with speech recognition since 1981. They have an interest in being able to automatically identify conversations and data. They may have provided wiretaps of conversations to Appen with the aim of improving software that can accomplish this," he told Volkskrant.