Haskins' teammates voted him as a team captain during training camp. He was photographed at a strip club without a mask last Sunday and apologized for the incident Tuesday.
"One thing I appreciated was his honesty in the conversation. He and I probably have talked five or six times in the past two days," Rivera said of Haskins.
Additionally, Washington fined Haskins $40,000, a source told Ian Rapoport of NFL Network.
The 23-year-old has started five games for Washington this season, including last week's loss to the Seattle Seahawks. The 2019 15th overall pick was filling in for veteran quarterback Alex Smith, who's dealing with a calf injury.
Rivera said Haskins is still the immediate backup plan if Smith is sidelined for another game.
Haskins has completed 62.9% of his pass attempts for 1,285 yards and five touchdowns against five interceptions this season. He's posted a 1-4 record in that span.
Washington - which currently leads the NFC East with a 6-8 record - will face the Carolina Panthers in Week 16.