The trio missed Arsenal’s Premier League opener against Crystal Palace last Friday, which they won 2-0, but will hope to be involved this weekend against the Foxes.
All three players had troubled pre-seasons as fitness issues prevented them from getting in shape.
Tomiyasu, who had calf problems last season, is struggling with a quad injury but played for Arsenal Under-21s last Saturday and trained with the first team this week.
Smith Rowe, meanwhile, has had a groin problem but he too has been training this week and will hopefully be in the squad for this weekend’s game with Leicester.
Of the three, Vieira is the most likely to struggle to make the squad as Arsenal carefully increase the intensity of their training after a foot injury.
Vieira was injured while on international duty in June and slowly improved his fitness over the summer.
The return of Smith Rowe, Tomiyasu and Vieira will give Arteta a headache for the weekend and going forward this season.
Ben White has impressed at right-back recently, giving William Saliba a start in the heart of defence, and Tomiyasu will provide more competition there.
Smith Rowe faces a fight for his place on the left flank after Gabriel Martinelli impressed in pre-season and scored last week against Crystal Palace.