The Leicester centre is battling to overcome an ankle injury and coach Stuart Lancaster insists he will not be given any extra time to prove he is able to take the field for the Calcutta Cup.
If Tuilagi is not ready in time, either Jonathan Joseph or Billy Twelvetrees will likely take his place in midfield.
Asked whether Tuilagi would be given until late in the week, Lancaster said: "No. You have to trust the players you have got and you have to be fair to the player.
"If he's not right to play an international game you don't pick him. It's the same for everyone. No (he will not get special treatment). You have to be fair to your team.
"We will see where he is Monday or Tuesday. Manu has gone back to Leicester to get some treatment.
"They have what is called an AlterG machine. The machine supports you in a harness and allows you to run without putting your body-weight through your legs.
"There are different options - you could put Brad (Barritt) at 12 and JJ at 13 or put Billy at 12 and Brad at 13."
Lancaster is keeping his cards close to his chest and did not give any clues to his preferred starting XV when England trained in front of 6,000 people at Headingley on Friday with both Twelvetrees and Joseph spending time running alongside Barritt.
Lancaster must also make tough choices at full-back, hooker and scrum-half.
"On the first day back in camp you could see the excitement of every player who is vying to get the shirt," said Danny Care, who is battling for the number nine jersey with Ben Youngs.
"No-one is nailed on for a start. It is great for English rugby that there is so much strength in depth.
"It is a good battle at nine. I am happy with how I have played but there is no indication yet of who will play. It keeps everyone on their toes."