Along with the recently returned Volkswagen, the Korean giant is expected to hit the tarmac, gravel and snow in 2013.
The report adds that unnamed racing parts-suppliers have confirmed the car is being built at the company's Offenbach headquarters in Germany, and is virtually finished.
Hyundai has yet to comment on the reports, adding to speculation that an announcement is imminent.
Hyundai's first foray into World Rallying began in 1999, with the ungainly Accent WRC. Piloted by Kenneth Erikkson and Alister McRae, the Hyundai World Rally team achieved solid but unspectacular results.
Their best individual result had been McRae's fourth and Eriksson's sixth in the 2001 Rally GB.
In 2002, the slate was cleared, with Juha Kankkunen, Freddy Loix and Armin Schwarz brought in to drive. They took the team to fourth in constructor's championship, edging out Mitsubishi and Skoda.
The team battled on in 2003 with a reduced budget and pulled out at the end of that season, vowing to return.
Hyundai may be holding off making the announcement until after the June 15 meeting of the World Motorsport Council.
The WRC plunged itself into more trouble last week by asking for huge increases in event fees from promoters, which is bound to produce casualties.
The FIA is asking organisers for a further €100,000 for 2013, almost doubling the 2012 fees of €140,000. Event organisers must sign up before the WMSC meeting.
Note: the i20 shown at the top of this article is the 2012 update, which is expected to hit Australia in the coming months.
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