Mourinho, 63, has been tasked with overseeing a major overhaul at Real Madrid following two trophyless seasons.
It’s understood that their defence is where the Mourinho will make most changes having already brought in Ibrahima Konate and Denzel Dumfries.
According to Sky Sport and SPORT BILD, Dortmund’s Schlotterbeck, 26, is another player Mourinho is keen on adding.
It’s been widely reported that the Germany international has a release clause in his contract that can be activated by certain clubs, with Real Madrid being one of them.
Speaking ahead of Germany’s World Cup opener against Curacao, Schlotterbeck responded to the rumours.
"Yes, of course you hear about something like that through the media, but fundamentally I've already said this a few weeks ago - the complete focus right now is on the World Cup, on the first match," he said.
“In Qatar, we saw how an opening game like that can go. It is extremely important, which is why even though I've heard about it, it's not in my head at all."