Crimestoppers has compiled the list with officers from the UK's Serious Organised Crime Agency (Soca) and Cypriot authorities.
One of the men is Martin Evans, 50, from Swansea, who is wanted for drug dealing, theft and fraudulent trading.
He ran a drug-dealing gang between 1999 and 2001, smuggling drugs into Britain and laundering the proceeds by converting cash into foreign currencies and moving it to the Netherlands to buy more drugs.
Evans is also wanted for stealing thousands of pounds of investments to a company he ran called Ostrich Centre Ltd. He fled after being freed from prison on licence in 2011.
Details of the remaining eight suspects are due to be released today.
Crimestoppers founder Lord Ashcroft said: "My hope is that we shall see success in bringing some of the fugitives to justice.
"While these suspected criminals will see Cyprus as a safe place to evade law enforcement, my belief is that with the help of the local public and expatriate community these individuals will not be able to escape justice for much longer."
The scheme, Operation Zygos, targets criminals living in the Republic of Cyprus or Turkish-controlled Northern Cyprus.