Both players picked up injuries in the 2-1 defeat against Manchester United on Sunday, with Agger suffering a bruised shin and Borini nursing a swollen ankle.
The outlook for the former initially looked bleak, with medial ligament damage suspected, but Rodgers later received welcome news on the Denmark international's condition and now believes he could play against the Canaries.
"Daniel probably has a good chance and Fabio is 50/50," Rodgers told reporters. "They haven't trained this week but we'll see how they go over the next 24 hours. They are responding well."
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"We wish him all the best," Rodgers said. "He's been fantastic for me since I've come in, so it's really unfortunate that he's got the injury. If he does [play again this season], it will certainly be towards the end [of the season].
"The good thing is that he is a real worker. We've got the operation done as quickly as we possibly could. He'll come back and recuperate and then we'll see how he goes.
"They talk six to nine months for these types of injuries, so even till then it will pretty much rule him out.
"But we will see. There's no pressure on him, he just needs to get fit and make sure the surgery goes well and we'll assess it into the New Year."
Also spending time in the medical room is Brazil international midfielder Lucas, but Rodgers revealed that the 25-year-old is making positive progress.
The former Gremio player pulled up with a thigh injury in the match against Manchester City in August.
"He has responded very well - he's doing great," the Northern Irishman stated. "He'll still have a wee bit of time away but he's working hard and working very well.
"He was in the pool today and he's got good movement; he's started to run. So hopefully he'll be back sooner rather than later."