The 21-year-old has caught the eye of some of European football’s top clubs after showing great potential in the Bundesliga.
Madrid sent scouts to watch the France Under-21 international, AS reports, and the youngster received glowing reports.
However, Diaby is likely to command a fee of at least €40 million if he leaves Leverkusen this summer.
The winger, who departed PSG for the German club in a €15m deal in 2019, has a deal until 2025 with his current employers.
But United and Bayern Munich have been monitoring his development and could battle the Merengues for his signature.
Diaby was forced to miss out on France’s start to the Under-21 European Championship this month after testing positive for coronavirus.
He's enjoying an impressive season with Leverkusen and has scored nine goals and provided 12 assists in 35 appearances in all competitions.
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