The trio missed Arsenal’s Premier League opener against Crystal Palace last Friday, which they won 2-0, but are hoping they could be involved this weekend against the Foxes.
All three of the players have had disrupted pre-seasons as fitness issues prevented them from getting match fit.
Tomiyasu, who had calf issues last season, has been struggling with a quad injury but played for Arsenal’s Under-21s last Saturday and has trained with the first-team this week.
Smith Rowe, meanwhile, has had a groin issue but he too has trained this week and will hopefully be in the squad for this weekend’s match with Leicester.
Of the three, Vieira is the most likely to struggle to make the squad as Arsenal are carefully increasing the intensity of his workouts after a foot injury.
Vieira picked up the injury while on international duty back in June and has slowly built up his fitness over the summer.
The return of Smith Rowe, Tomiyasu and Vieira will give Arteta selection headaches for the weekend and moving forward this season.
Ben White has impressed at right-back recently, which has allowed William Saliba to start in the heart of defence, and Tomiyasu will provide further competition there.
Smith Rowe faces a fight for his spot on the left flank after Gabriel Martinelli’s impressed in pre-season and scored last week against Crystal Palace.