Italy's Autosprint said it believes the former Lotus team's new single seater – to be called the CT01 and believed to have passed the FIA's crash tests – could be unveiled "at the end of January".
That would be even earlier than some other teams intend to launch their cars, ahead of the start of the official test season at Jerez on 7 February.
Germany's Auto Motor und Sport, meanwhile, said that while the former Renault team Lotus F1 has not yet revealed a launch date, the 2012 car is "very likely" to get its track debut at Jerez.
The magazine said the car, to accommodate Kimi Raikkonen's return this year, passed the FIA's mandatory crash tests earlier in January.
Auto Motor und Sport also reports that following the departures of bosses Colin Kolles and Geoff Willis, "delays" at HRT could force the struggling Spanish team to once again start a new season with its old car.
01/18/12 Formula One's 2012 car launch season kicks off on February 1st. McLaren will be the first team to take off the wraps of their car.
1 Feb – McLaren (Woking)
3 Feb – Force India (Silverstone)
3 Feb – Ferrari (Maranello)
6 Feb – Sauber F1 Team (Jerez)
6 Feb – Red Bull (Online)