The Augsburg full-back is said to be a key transfer target for Jose Mourinho this summer.
The Chelsea boss has admitted he is interested in signing a new left-back with Filipe Luis set to leave for old side Atletico Madrid within the next couple of days.
And recent reports have linked the Blues with a move for 21-year-old Rahman.
He impressed in the Bundesliga last campaign and is said to be interested in moving to Stamford Bridge.
But now Marca claims that Real Madrid have entered the race for his signature.
Raga Benitez has reportedly added him to his list of possible transfer targets as he aims to strengthen the left side of his defence.
Jose Mourinho recently confirmed that he was in the market for a left-back.
Source: Daily Star