The team's latest offer to the impending free agent is worth more than $45 million over three years, according to Mike Klis of 9News.
Osweiler will become an unrestricted free agent on Wednesday if no deal is reached before then.
The four-year pro has seven career starts, all coming during the 2015 regular season after he took over for Peyton Manning. Osweiler completed 61.8 percent of his passes with 10 touchdowns and six interceptions over that span before ceding the starting job back to Manning and watching him lead the team to a win in Super Bowl 50.
Manning is expected to announce his retirement in the coming days. If Manning opts to continue his career, the Broncos are expected to cut him.
With a $15-million per year offer to Osweiler, it's clear the Broncos believe their younger quarterback has the upside to be a high-end, if not elite, starter in the NFL for years to come.