Summer signings José Córdoba and Ben Chrisene are expected to be available for the visit of Blackburn Rovers on Saturday.
City's first home game of the 2024/25 Championship season sees Rovers arrive at Carrow Road on the back of a 4-2 win on the opening night.
Head coach Johannes Hoff Thorup has provided an update on the Norwich City squad ahead of the game.
"Christian Fassnacht and Jacob Sørensen will be out for a while, I think we're talking a handful of weeks. A foot injury for Lungi and Achilles for Fasi," he said.
"(José Córdoba and Ben Chrisene) are both in training, the plan is they'll be around the team for Saturday and we'll see how many minutes they will be able for.
"(Ashley Barnes) not in training yet. From what I hear, it's going a little better than expected but the plan remains the same. We want him ready for game minutes after the first international break."
His first win as City boss came in midweek as the Canaries beat Stevenage 4-3 in the first round of the Carabao Cup.
Crystal Palace await in the second round at the end of the month, but for now Hoff Thorup's attentions have returned to league football.
"We scored four very good goals which was a step in the right direction. There are a lot of details for us to improve but that's a good step.
"We will celebrate if we win but we'll quickly dig in to small details if the performance is not good enough. Players need to see a coach coming in who isn't affected by results at the weekend, but affected by performance," he explained.
John Eustace's side have scored 10 goals in their opening two games of the season, adding a 6-1 League Cup triumph to the win against Derby.
"They started well, they're scoring a lot of goals. But there's parts of the game where we see that we can hurt them and put them under pressure.
"With training today and tomorrow, we need to make sure we are ready to go out and perform with the intensity that the crowd expect to see."