A week ago the Broncos lost starting right tackle Ja'Wuan James for the season after he tore his Achilles while working out.
Fleming, 28, will sign a one-year deal worth up to $3.67 million.
Fleming spent the 2020 season as the Giants’ starting right tackle, playing all 16 games. Last season was his first as a full-time starter.
Fleming entered the league as a Patriots’ fourth-round pick, spending four seasons with the franchise. He then spent two years with the Cowboys before joining the Giants.
In seven seasons, Fleming has played 91 games with 42 starts.