Julen Lopetegui was axed on Monday after a disastrous start to his tenure, culminating in the 5-1 trouncing at the hands of Barcelona on Sunday. Santiago Solari has been placed in temporary charge, but the European champions want Martinez to step in eventually, according to Pete Jenson and Dominic King of the Daily Mail.
It's added former Chelsea and Italy manager Antonio Conte was initially in line to take over from Lopetegui, as he is unattached following his departure from the Blues in the summer.
"Sportsmail understands that key figures within Madrid's dressing room were opposed to the appointment of the Italian which prompted the club's hierarchy to scrap that plan," said King and Jenson. "That now means Martinez could be given the opportunity to revive the campaign of the reigning Champions League holders."
Although Martinez is said to be the leading candidate, it's noted Madrid have yet to make an official approach to his representative or the Belgium Football Association.
It was reported by Cadena Ser (h/t Sport) that Belgium would not resist any approach from Los Blancos for their coach.
Martinez was asked about the speculation on Tuesday but didn't pass any comment on interest from Madrid, per Kristof Terreur of Het Laatste Nieuws:
The appointment would be a surprise. After all, while Martinez has done well during his time with Belgium, steering them to third at the FIFA World Cup in the summer, his record in club management is not as impressive.
While he won the FA Cup with Wigan Athletic in 2013, the team were relegated in the same season. He was then appointed Everton boss and after an excellent first term in charge, he was sacked at the end of his third campaign following a torrid run of form.
BBC Sport's Greg O'Keeffe believes while he has had past issues in club management he could suit Real Madrid:
Greg O'Keeffe @GregOK
You'd maybe think it unlikely (Catalan!) Roberto Martinez would get Real Madrid job until you recall he joined Everton after Wigan went down, then Belgium after Toffees sacking. One thing for certain he'll impress at interview & his attacking style might work with the Galacticos
Madrid are a team in need of a rejuvenation, as they sit in ninth place in La Liga.
Although they were competitive at times during the match with Barcelona on Sunday, the manner in which they capitulated in the final stages was indicative of the woes they've had this season. Whoever does come in will have a big job to do to lift spirits and push them up the table.
Even so, there's undeniable quality and plenty of leaders within the squad. Martinez's positive approach and enterprising brand of football may be an ideal tonic for Madrid, in the short term at least.