Henshaw has been struggling with a hamstring injury and missed Ireland's opening Pool D win over Canada, with Luke Fitzgerald taking his place at inside centre.
It was hoped Henshaw would be ready to return to play against Romania but he is still battling the injury and did not train fully on Wednesday.
Skills coach Richie Murphy admitted the Connacht centre will be assessed in the build-up to the Wembley clash but his inclusion at this stage remains uncertain.
"Robbie trained reasonably hard today, he did a lot of running and a lot of passing," said Ireland assistant coach Murphy.
"Again he's in a position where he's returning to full fitness and he's very close. Whether Robbie will be ready for this week we're not quite sure at this moment, but we're hoping that he will.
"He trained quite a lot today and he'll probably have to train back with the team in our next training session, which is on Friday."
Meanwhile, Johnny Sexton, Peter O'Mahony and Iain Henderson all missed Ireland's training session at St George's Park as a precaution due to minor knocks, but they are all expected to be fit for Sunday.