Julen Lopetegui's sacking on Monday means that the reigning European giants are on the lookout for a new manager, with Italian Antonio Conte having been heavily linked with the role.
However, with any move for the former Chelsea manager complicated by the fact that he is still under contract with the 'Blues' and with Conte seemingly ruling himself out of the running earlier this week, 'Los Blancos' have been forced to weigh up alternatives.
One of their options is understood to be Martinez, who has impressed with the 'Red Devils', guiding them the third place at the World Cup in Russia earlier this summer.
It is believed that Martinez, although Catalan, would be very interested in taking over at the Bernabeu and would be likely to accept the job if it was offered to him.
Nevertheless, Belgium plan on doing their best to keep their head coach, with a sourc eclose to the national team telling 'Sky Sports': "Roberto has a contract with the Belgian Football Association (KBVB) until 2020 and anyone intending to make an approach for the manager would need to do that through the Association in the first instance."
There is not believed to be a release clause in Martinez's contract with Belgium, meaning Madrid will have to agree a compensation package with his current employers in order to be able to speak to him.
Martinez's close relationship with Eden Hazard, a reported target for Real Madrid, is understood to be a factor in his appeal.
Santiago Solari is current in interim charge of Real, but with Spanish league rules saying a caretaker boss can only be in charge for a fortnight, Madrid have until only November 12 to find a new manager.