The 24-year-old, capped 32 times by England, has been out of action since November with a knee injury.
However, it is understood his recovery has progressed quicker than expected.
Vunipola could now be in contention to face Scotland on 11 March, or Ireland a week later.
He was one of England's outstanding performers throughout their unbeaten year of 2016, and his ball-carrying and dynamism has been missed by Eddie Jones' side.
There were initial fears Vunipola would miss the whole of England's Six Nations title defence, but it is understood he has looked sharp on his return to full training this week, and is targeting a quick return to international rugby.
Vunipola's older brother, Mako, recently made his own comeback from a knee problem, and came off the bench in the win over Italy.
England number eight Billy Vunipola is set for a shock early return to action for his club Saracens against Newcastle on Sunday, boosting his hopes of a 2017 Six Nations call-up.