Healy, who made seven GUINNESS PRO12 appearances last season, has undergone other surgeries in the past 18 months, namely on his ankle and hamstring, before the neck problem flared up earlier this year.
But Schmidt insists the 27-year-old will be given every chance to prove his worth.
"We are very much working week-to-week with Cian," said Schmidt. "He is fully participating in some sessions. He also did an individual session so he is mixing that up.
"We are just hoping the picture gets clearer as we get closer so we can make a decision that would see him fully fit to start the tournament, even if he doesn't play prior to it.
"One of the things is we play (England in Twickenham) two weeks before the first game. If we thought that he might not be fit for England but would be fit by Canada, that would be part of the decision-making process."
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