Rivers limped off the ground midway through the first quarter of the Cats' win against the Western Bulldogs at Etihad Stadium on Saturday night and did not take any further part in the game.
Scott said the Cats' preliminary diagnosis was Rivers had a slight medial ligament strain.
"He had an issue with the back of his knee after round one, missed a few, came back and he's got an issue with a different part of the same knee," Scott said after Saturday night's match.
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"[Our doctors] say it might be a slight medial at the moment. They're not too worried about it, but they're reserving their diagnosis until they've got a bit more information."
Cats midfielder Josh Caddy also played no part in the second half against the Bulldogs, after copping a heavy knock to the head from Bulldogs defender Brett Goodes.
A free kick was paid against Goodes and Caddy took the kick, but left the ground soon after.
Scott said Caddy had seemed okay at first after the knock, but it soon became apparent he had concussion.
"It seemed incredibly minor. [Our doctors] wanted to be cautious first and as sometimes happens with these things he actually got worse before he got better," Scott said.
"So the doctors made the call straight away (that Caddy would not return to the field] which is the right thing to do."
Scott was confident Tom Hawkins, a late withdrawal from the Bulldogs game with back soreness, and Paul Chapman (hamstring) would be fit to play against Richmond next Saturday.
"[Tom] had an issue through the week that we thought meant he was going to struggle to come up, but we decided to name him and give him right up until the game before we made that decision," Scott said.
"But we just don't take risks with guys that are sore. And he's had a little bit of a back issue, he's just got a tight back and he hasn't been moving all that well and we just decided he wasn't quite good enough this week."
Scott said Chapman had suffered a slight hamstring strain before half-time against the Sydney Swans last Friday night.
"He was able to play the game out, but couldn't run 100 per cent this week at training so we don't play those guys," he said.
"[We're] confident he'll be right next week."
Nick Bowen is a reporter with AFL Media. Follow him on Twitter: @AFL_Nick
