Sanders, the 2007 defensive player of the year, could return to practice this week and Addai lobbied to play in Sunday's 34-14 loss at Green Bay despite an injured hamstring.
Dungy isn't sure how many more games they'll miss.
"It's hard to say," Dungy said when asked about Addai. "He wanted to try and go last week, but we thought maybe, with the extra day (off) this week, it might help him."
As for Sanders, Dungy said: "We're hoping he can get back out there and practice this week. We'll have to see."
Sanders hasn't played since spraining his right ankle in Week 2 against Minnesota. The injury was diagnosed as a high ankle sprain, which typically keeps players out four to six weeks.
Sanders also had arthroscopic knee surgery while he was out, something Dungy has said would not delay Sanders' return.
Addai was expected to miss up to a month after hurting his hamstring in the first quarter of Indy's 31-3 victory over Baltimore last week. There were reports that Addai had a partial tear, something Dungy has denied.
Also, the Colts could get starting cornerback Kelvin Hayden back soon. Hayden had surgery to repair the meniscus in his left knee after Indy's comeback victory at Houston on Oct. 5, and hasn't practiced since then.
While this could be the week all three players return, with Indy (3-3) needing a victory at Tennessee (6-0) on Monday night to stay in the AFC South title chase, Dungy isn't making any guarantees.
"Kelvin has been running and rehabbing a little bit," Dungy said. "But I think we have to go into the game, thinking we'll have none of them."