Russian news agencies, quoting unnamed officials involved in the inquiry, say the huge Mi-26 helicopter was hit by a rocket fired from a portable launcher.
Some reports say the commission's findings are final, but another source from the Russian Defence Ministry's forensic research centre was quoted as saying the investigators needed another two weeks to complete their work.
Chechen rebels have already said that they shot down the helicopter, and a used missile launcher was also reported to have been found close to the crash site.
The crash - which Russian media has called the "Second Kursk" - resulted in the biggest single military loss of life since Moscow sent its forces back into Chechnya in 1999.
It has led to the suspension of the Russian army's aviation commander and calls for major military reforms.
Experts say it is also a huge embarrassment for President Vladimir Putin, who has repeatedly said the war in Chechnya was over.
'Overloaded'
The helicopter crashed onto a minefield outside the Russian army headquarters in Grozny after its right engine caught fire.
The source from the forensic research centre said the investigators still needed more time to finish examining the helicopter's engine and deciphering the flight recorders' data.
Mil Mi-26
Investigators were pursuing two theories, a technical malfunction and a rocket attack.
But the BBC's Nikolai Gorshkov in Moscow says it appears now that the missile theory has prevailed.
The use of Mi-26 transport helicopters in Chechnya has been banned after the incident and amid reports in the Russian media that the helicopter was overloaded.
It also appears that it was flown despite an order by the Russian Ministry of Defence specifically banning its use for transporting the personnel.
Defence Minister Sergei Ivanov told reporters he had found violations of flight procedures, promising a full and swift investigation and compensation for victims' relatives.
However, he dismissed reports that the helicopter had been overloaded as "absurd".