Los Blancos boss Zinedine Zidane is looking to bolster his attack in the summer and Werner has emerged as a target as he continues to go from strength to strength for the Bulls.
The German international has fired home 24 goals for club and country this season to take Leipzig to the top of the table and his form is attracting plenty of interest.
English Premier League duo Chelsea and Liverpool are keeping tabs on Werner's situation and now Real can also be added to the list of admirers.
Karim Benzema continues to bang in the goals for Los Blancos and has recently penned a new deal but support is needed and Werner could be the man to provide it.
Not only that, he would be in with a chance of dislodging Benzema, and that is the kind of competition that Zidane is after.
Luka Jovic has not turned out to be the answer following his switch from Eintracht Frankfurt in the summer, but that has not deterred Real from looks towards Germany for new signings.
Leipzig will not be willing to sell Werner this month as they battle for the title, but Real could have a chance at the end of the campaign if the offer they make is big enough.
The Germans have just secured Werner to a bumper new deal so will be under no pressure to cash in any time soon.