He left the field on Saturday with a groin complaint. A decision on his fitness will be delayed until just before kickoff.
"Bill is progressing nicely," said coach Darren Bazeley.
"We will give him as long as we can ... although if he is not completely right we won't risk him."
Tuiloma is hugely important to this team.
The Olympique Marseille player looked the most assured in possession on Saturday and is the vital shield in front of the defence. He is probably the least expendable in Bazeley's squad but with or without the No6 the New Zealanders don't seem to lack belief.
"I feel very confident and we are prepared for the game," said defender Adam Mitchell.
"We deserved a point [on Saturday] but we weren't happy with it.
"We want to get the ball down more and play ... we will bring the game to the USA and try to make history."
Mitchell and fellow central defender Sam Brotheron will be key figures, as they try to negate the threat of Emerson Hyndman (Fulham) and Rubin Rubio (FC Utrecht).
The American striking duo were the most impressive performers in a sometimes scratchy 2-1 win against Myanmar, where they took a long time to gain control of the match.
"They are a good footballing team, they have some good individuals and play a slightly different style to Ukraine," said Bazeley of the US.
"But we have watched their last four games and we will be ready to deal with what they throw at us."
Meanwhile, Bazeley is confident their woes in front of goal - the Junior All Whites blew several clear-cut opportunities on Saturday, particularly in the closing stages - won't haunt the individuals involved.
"It's tough for those guys - who feel like they could have been the hero - but that's football.
"We move on pretty quickly. I know if [they] had those chances again they would put them in the net. I'm very confident in them."
