Captain Jamie Peacock is responding to treatment for his knee injury ahead of England's Four Nations match against New Zealand on Saturday.
The experienced Leeds Rhinos forward suffered a knock during the 36-20 defeat by Australia last Saturday.
James Graham and Gareth Ellis, who both experienced lower back spasms, are also currently having treatment.
"It is too early to say whether they will be fit for Saturday's game," said England coach Steve McNamara.
"They are under intensive treatment. We are not stressed at this stage about it.
"We have fantastic personnel ready to come in if these guys don't make it, but we will give them every opportunity to do so."
The squad had a day off on Monday ahead of preparations for their crunch meeting with the New Zealanders at the KC Stadium.
The two teams are level on points after beating Wales and losing to Australia and also have the same points difference.
But the Kiwis have a superior points percentage and need only a draw against England to set up a meeting with Australia in the final at Elland Road in Leeds on 19 November.
Stand-off Kevin Sinfield believes England can draw plenty of encouragement from the Australia clash.
He said: "It's straight knockout now for us.
"We can take some confidence from Saturday. At times we troubled the Aussies and it would be great to get another crack at them.
"We know we've got to do better. We needed to improve a whole lot on what we did against Wales and we weren't quite there in some areas.
"We know the standard now. I thought we troubled the Aussies in some aspects but we weren't disciplined enough and paid the price."