Centre Tuilagi remained with the England squad after suffering a groin injury in the opening defeat in France, although he did not feature as the Rugby World Cup finalists bounced back against Scotland.
The Leicester Tigers star should be able to feature at Twickenham a week on Sunday, though, head coach Eddie Jones revealed.
England faces Ireland, which has won two matches from two so far - beating defending Grand Slam champions Wales last week - to join France at the top of the Six Nations table.
Alongside Tuilagi, England could be boosted by a return for Henry Slade, the 26-year-old having been out with an ankle injury since December.
"Manu is looking very good," Jones told Sky Sports News. "Very promising. He should be in full training by the start of next week.
"Henry Slade ran today and we've yet to get a medical report. It's definitely promising but too early to say whether he will be alright for Ireland or not."
However, Watson - another man, like Slade, yet to feature in the campaign - is still struggling with a calf injury picked up on the eve of the competition.
"Anthony Watson is still a couple of weeks away," Jones said.