In June, Antoine Deltour and Raphaël Halet received 12- and nine-month suspended sentences respectively for leaking documents that exposed huge tax breaks for major international companies being given by the Luxembourg government.
They were also fined €1500 and €1000, respectively.
Prosecutors in Luxembourg on Tuesday called for tougher sentences for the pair but their defence lawyers are calling for an acquittal, arguing the leaks were a form of public service.
Both Deltour and Halet were former employees of accounting firm PricewaterhouseCoopers, which was working with companies such as Amazon, Apple, Gazprom and Ikea on their tax arrangements with Luxembourg authorities.
If convicted, both face imprisonment but Deltour, considered the main whistleblower, is facing up to 10 years in jail and a maximum fine of €1.5m.
The Luxembourg prosecutors also want to challenge the acquittal of French journalist Edouard Perrin, who was sent the documents by Deltour and Halet.
The decision to launch a general appeal against all three verdicts could also have consequences for Perrin, a journalist with France 2 television who based his expose on thousands of documents obtained by the other two defendants.
The Luxleaks scandal sparked howls of protest in Europe, leading to a crackdown on the generous tax deals the wealthy seemed able to arrange with governments, as people struggled with tough austerity policies.
The revelations were doubly embarrassing since they showed many of the tax deals were made during the long-time premiership of Jean-Claude Juncker, now President of the European Commission.
The appeal hearings are likely to be held by the end of the year.