The 26-year-old picked up a knee injury in training last Thursday which kept him out of Hull's last fixture away at Huddersfield Town.
Despite reports that he could now face a spell on the sidelines, Bruce has claimed that the midfielder could be available for selection for the visit of Watford to the KC Stadium.
"He jarred his knee and was uncomfortable over the weekend. He had scans on Friday and there's nothing too serious. Hopefully he might be available for Tuesday," said Bruce.
Quinn joined Hull last year from Sheffield United.