Flanker Peter O'Mahony took part in some running yesterday as he continues to follow the graded return to play protocols, while Earls is due to see a specialist today regarding his shoulder.
Regarding Earls, team manager Michael Kearney said: "He presented kind of poorly enough post-game, but the prognosis at the moment is that he has a sore shoulder.
"There doesn't appear to be any major ligament damage or anything like that, so the medics would be hopeful that he would be available. We would be hopeful that come Friday they'll all partake fully in training and be available for selection."
Four players - Darren Cave and Andrew Trimble from Ulster, Connacht youngster Robbie Henshaw and Leinster's Rhys Ruddock - have been added to the training squad this week ahead of the visit of England to the Aviva Stadium.
Should D'Arcy and Earls fail to recover in time, Brian O'Driscoll, the man-of-the-match against Wales, and Fergus McFadden were mentioned as possible starters at inside centre.
"Brian played in the first Test in New Zealand at first centre, so that's an option. Fergus McFadden played there for Leinster, so they would be the two options being considered at the moment," admitted Kearney.
They ran in seven tries against Argentina at the end of November, and will be eager to cross the whitewash at the Aviva Stadium again this weekend after failing to do so in their last two clashes with England.
Giving his take as a member of the management team, Kearney said: "I think there a number of reasons for the improvements. At our camp in August the players realised they needed to acknowledge the step-up between provincial and international rugby and needed to up standards.
"And the addition of a new coach in Anthony (Foley) has helped too. It's a mixture of both."
Foley's call-up to the coaching staff to oversee Ireland's defensive structures has allowed Les Kiss to focus specifically on attack after the Australian had been maintaining a dual role for a period.
The benefits has been felt by the players according to scrum half Conor Murray who explained: "Separating the two roles has been good I think. You saw quite clearly in the first half (against Wales) we were mainly attacking and we were able to build up quite a lead.
"And in the second half, once Wales got into our faces, we showed great determination to hold them out. It's also of benefit to be able to go to a coach and have a specific chat about something.
"If you're unclear, that's his specific role and you'll get a clear answer. Our attack and defence are both in good positions, which I think you can put down to the separation of powers. That, and the players taking things on board."