The explosive 21-year-old was forced home from the Grand Slam champions' tour of Australia early, after breaking a bone in his hand during the first Test defeat in Brisbane.
It had been feared that Faletau could be sidelined for an extended period but the Dragons are confident their starlet will be back in action for the beginning of the season.
Steffan Jones and Adam Jones have also returned to training, having missed the end of last season with ankle and foot injuries respectively, while Tonderai Chavhanga is scheduled for a return in August.
"Everybody is in great shape," head coach Darren Edwards told the South Wales Argus.
"The squad were given targets when they left and have hit them.
"I'm particularly impressed with the guys from the Premiership that we have invited in to join us in training - they are standing toe-to-toe with the rest of our squad.
"Credit to them for their hard work, they want to play professional rugby and their desire is certainly spurring on our current pros. That competitiveness is what we want to generate.
"Unless we are unlucky in pre-season we will be starting with a full squad, which is great for preparation and a huge boost."