The Belgium international has been in fine form for the Portuguese outfit both domestically and in Europe, catching the eye of the Santiago Bernabeu giants
Los Blancos are in the market for a new player in the centre of the park due to the ongoing uncertainty over the future of Nuri Sahin.
Santiago Bernabeu head coach Jose Mourinho allegedly believes Witsel could be a valuable addition to his squad, with the Turkey international potentially leaving at the end of the season.
The 23-year-old midfielder is a product of the Standard Liege youth academy, but left the Belgian team for Jorge Jesus' men at the start of the current season.
He has since developed into a key player at the Lisbon giants, and his good form has now earned him the interest of the Spanish capital-city side.
Witsel will not be available on the cheap though, as he has a contract until June 2016. The versatile midfielder reportedly has a buyout clause of €40 million.