According to the British publication The Sun, the France international who cost an initial $36 million to United, would be offered at $60m. [Mourinho defends Man United's performance against Everton]
The report also said Madrid could include a player in the deal.
A further $8 million is on Martial's current contract at United if he scored 25 goals for coach Jose Mourinho's side this season and that same amount once he earns 25 caps for France.
Madrid could offer forward James Rodriguez in a swap deal with coach Zinedine Zidane unwilling to accommodate the Colombian in his side.
With France's Paris Saint-Germain also being linked to Martial this week, United certainly seem to be facing a fight to keep the star at the club.