Modkins reportedly followed all protocols and notified the Broncos after finding out a family member tested positive, according to NFL Network's James Palmer.
Curtis is currently self-isolating at home while the team communicates with the NFL.
"The Broncos remain in regular communication with the league office, NFL Chief Medical Officer Dr. Allen Sills and team medical staff. We will take all necessary precautions to ensure the safety of our team, opponents, and community."
Denver is currently scheduled to face the Patriots on Sunday in a matchup that was originally slated for Week 5 but got pushed back to Week 6 due to the Pats' positive test results.
New England had another positive result Friday and closed its facility as a result, but the franchise later reopened the building on Saturday.