The suspects, who were taken into custody Thursday, were identified as three Iranian nationals who allegedly kidnapped Yazdi, 44, from the United Arab Emirates June 25, the British newspaper the Guardian reported Friday.
Yazdi, who holds both British and Iranian citizenship, owns a general trading company in Dubai and has lived there for about 10 years.
A British Foreign Office spokesperson said: "We welcome the arrests of three men by the Emirati authorities in connection with the alleged kidnapping of British-Iranian national Abbas Yazdi. The U.K. will continue to liaise closely with the Emirati authorities on the investigation."
Yazdi's wife, Atena, has accused the British Serious Fraud Office of supplying the Iranian government with information on her husband's whereabouts that led to his kidnapping. Iran's state general inspection organization, which was investigating Yazdi for bribery involving the Norwegian oil giant Statoil, said it requested information from the SFO about Yazdi in February 2013.
The issue has been raised by shadow attorney general Emily Thornberry MP, who noted the United Kingdom and Iran have no diplomatic relations.
"What are the rules governing interactions between U.K. prosecutors and their counterparts in countries where diplomatic ties have been renounced? Was co-operation between the SFO and the Iranian authorities a regular occurrence during the period that ties were broken? Has the SFO, or the Crown Prosecution Service for that matter, recently assisted any other regimes that the U.K. government does not recognize and/or that practice or are suspected of practicing extrajudicial execution?" Thornberry wrote in a letter to Attorney General Dominic Grieve.
Despite reports from the British Foreign Office that her husband was killed during the kidnapping, Atena Yazdi said she believes her husband is still alive.
"I am extremely happy about the news of these arrests. It made me and our children so happy that the investigation is going at least one step forward. We now look forward to hearing any information that these detainees could provide on where Abbas has been taken and what have they done to him," she said.
"We also hope that the U.K. government engages more in this case and negotiates with Iran about Abbas. We have no doubt that the people who have been arrested had direct involvement in Abbas' disappearance."
Celebrity Breakups and divorces of 2014 [PHOTOS]