Following the return of Cristiano Ronaldo to Old Trafford, the 25-year-old has fallen down the pecking order, starting in just two of the Red Devils' opening eight matches across all competitions.
Martial has been identified by Dortmund as a possible replacement for Erling Braut Haaland, who could be on the move next summer when his release clause, valued between £64m and £86m, becomes active.
However, according to SPORT1, United value the Frenchman between £42m and £47m and Dortmund are not prepared to pay such a fee, or offer the forward a salary close to the current £200,000 a week he earns in Manchester.
Dortmund are understood to have around 30 scouts spread out across Europe searching for a potential Haaland replacement and, along with Martial, they have identified Nice forwards Amine Gouiri and Kasper Dolberg as well as PSV Eindhoven youngster Noni Madueke.
Martial, who has four years remaining on his contract at Old Trafford, has made 264 appearances for United across all competitions, scoring 78 goals and providing 50 assists.