According to the Herald Sun, Langdon flew into Melbourne on Monday to continue talks with the Demons, ahead of a move to the club during the upcoming trade period.
Langdon will make the move after five seasons and 68 games for Fremantle, which culminated in a career-best season in 2019.
The speedster averaged 25.0 disposals, 6.0 marks, 3.6 inside 50s and 3.0 rebound 50s per game this season, after featuring in all 22 matches for Fremantle.
Melbourne will need to trade for Langdon, with the Demons currently owning picks 2, 20 and 38 in the draft.
The Demons have reportedly told clubs they are open to traded pick two in exchange for two first-round picks – one of which could be used to bring Langdon to the club.