The Wales full-back, who scored 24 points in a 34-7 drubbing of Scotland last weekend, missed Friday's captain's run in Surrey due to feeling unwell.
A Wales spokesman confirmed Halfpenny's absence from the session.
Should the Scarlets star not recover in time, then Wales head coach Warren Gatland could consider promoting Cardiff Blues' Gareth Anscombe as a straight replacement off the bench.
Fly-half Rhys Patchell, meanwhile, has excelled at full-back for the Scarlets this season.
Halfpenny, who has won 75 caps, is approaching 700 points for Wales and is an integral part of a team seeking to inflict a first Six Nations home defeat on England since the 2012 tournament.