The 21-year-old struggled to maintain a first-team spot under Jose Mourinho last season, starting just 18 Premier League matches.
In total, the Frenchman scored eight goals and created six assists in 41 appearances in all competitions.
Due to Mourinho's reluctance to give the forward a regular role, speculation has emerged over his long-term future, but Martial has responded on Twitter by writing: "The rumours are false."
The tweet, which was penned in his native language French, does not directly mention the reports about his United future, but the timing of it suggests that he is alluding to such matters.
Martial joined the Red Devils from AS Monaco for a reported £36m figure in 2015.