Broncos general manager John Elway last week told Manning, who turns 40 in March, to take his time on making the career decision.
According to Mike Klis of KUSA in Denver, the Broncos have not started contract negotiations with Osweiler "out of respect to Manning."
Manning became the oldest quarterback to win the Super Bowl when the Broncos upset the Carolina Panthers 24-10 at Levi's Stadium in Santa Clara, Calif.
Manning completed just 13 of 23 passes for 141 yards and an interception -- a 56.6 passer rating -- but the Broncos' outstanding defense shut down Panthers quarterback Cam Newton, sacking him six times, to give Manning the second Lombardi Trophy of his Hall of Fame career.
Most people expect Manning to retire, just as Elway did after winning back-to-back championships with the Broncos in the 1997 and 1998 seasons.
Osweiler, 25, is set to become a free agent when the new league year begins on March 9 and several teams could be lining up to give Osweiler a significant payday.
Osweiler started seven games this past season and went 5-2 after filling in for an injured Manning.
Manning's $19 million salary for 2016 guarantees on March 9, so the deadline clock is ticking.