Sam Burgess could make his first Bath appearance as early as this Friday.
The 25-year-old is back in training less than two months since fracturing a cheekbone and eye socket during his NRL grand final appearance for South Sydney.
And his union debut could come against Harlequins in this week' Premiership game.
"It might be a possibility," Bath coach Mike Ford said. "We haven't decided on the team for Friday yet. We will keep a close eye on him over the next few days to see where he is.
"We are just waiting for Sam to tell us when he feels ready. He had a great session on Tuesday, but with him we just need to take it day by day."
Burgess crossed codes in the autumn with the aim of playing for England at a World Cup - perhaps even next year's.
But it is not yet clear where he will be asked to play at centre or as a back-row forward, and several high-profile commentators have warned 2015 could come too soon.
Speaking in September former England captain Lewis Moody said: "There's always a chance for him, but I think the World Cup will be far too soon. But that won't be down to coaches or other players, it will be down to Sam and how quickly he fits into the game."