The 22-year-old has struggled to hold down a regular place in Jose Mourinho's team over the last few seasons.
In the current campaign, Martial has started 16 Premier League games and has come off the bench in a further 10, contributing nine goals and five assists.
The footballer's representative Philippe Lamboley told IlBiancoNero: "I can't confirm Martial will remain at Old Trafford next season, I am sorry but I can't add anything else about it.
"Martial's objective is to win the FA Cup and to finish in second place with Manchester United. That way the Red Devils would qualify for the Champions League."
Martial moved to the North-West outfit from Monaco in 2015.