Dortmund currently sit in sixth place in the Bundesliga and 12 points off top spot, and it had been suggested that Tuchel would look to make changes to his squad this month.
The 43-year-old told ESPN: "I don't think that we add somebody [in January]. We had a lot of new players and it all takes time [to settle]. Even the German guys, who have a lot of experience, you have to admit that it took its time for them [to settle]. Every change in a club takes time.
"Right now, the group is growing together. We had to change a lot because we had too many injuries. We wish for more players to be healthy, more players on the pitch who can play week after week, they need those minutes. Right now, we don't want to add somebody. [Zelalem?] Right now? No. Not as far as I'm concerned."
Zelalem has been restricted to just 17 minutes of EFL Cup action with the Gunners this season.