Scarlets full-back Halfpenny has not played since suffering concussion when Wales beat Australia on November 10.
Wales released Halfpenny back to the Scarlets for last weekend’s Guinness PRO14 appointment with Benetton, but he was not included in their match-day 23.
Wales assistant coach Robin McBryde said: “They are training with us, so hopefully they will be fit enough for selection.
“Leigh was released, but didn’t play, last week. We just felt that he needed a little bit more contact, so that is what he is going to have.
“We will measure both of them as the week goes on.
“With Leigh, it is an individual case, and those discussions would take place with the medical team, the coaches and Leigh himself.
“There is no way that we would put somebody in a position that he is not comfortable with. Those discussions will take place during the week.”
Both Wales and England are unbeaten after two rounds of the championship, with Saturday’s clash being billed by many as a title eliminator.
Wales are also on an 11-match undefeated run, with one more victory required to break their all-time record set between 1907 and 1910.
McBryde added: “It’s a big game. England are riding high on the back of two very good performances.
“We’ve had the results, but maybe not the performances, so we have got a bit of work ahead of us.
“They (England) have started really strongly (against Ireland and France), so we have got to be able to weather the storm.
“Obviously, they have got a big kicking game that we have got to contend with, but we have got to focus on ourselves.
“It is a big test, and we are going to have to be at our best.”
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