The Sun says it is a dramatic double swoop as under-fire boss Rafa Benitez desperately seeks to turn around a disastrous season.
Former Manchester United idol Van Nistelrooy, 33, is out of contract at the end of the season and is out of favour at Real.
The only remaining detail to be sorted out is whether Liverpool will pick up the hitman's whopping £140,000-a-week pay package.
Benitez wants Madrid to pay part of his salary but the Spanish giants insist on getting him off their wage bill.
Van der Vaart, 26, was told he is surplus to Real's requirements in the summer but he has fought back to earn some playing time and has impressed.