Tevez made a shock transfer request in December, blaming bad relations with the City management, but withdrew the demand later in the month after clear-the-air talks with the Premier League club.
Real Madrid had already contacted City, Marca said.
There were two big hurdles, the paper said: firstly, that City would insist on a transfer rather than a loan, and secondly that a transfer would cost 40 million euros and the Argentine's annual salary was eight million euros.
Hamburg has rebuffed Real Madrid's efforts to bring over 34-year-old Van Nistelrooy, saying he will not be allowed to leave and must complete his contract.
Real Madrid are trying to fill the gap left by Gonzalo Higuain, who could be out of action for another four months following surgery on January 12 for a slipped disc and may not return to full fitness for a year.
Real are four points behind Spanish first division leaders Barcelona after a shock 1-1 draw at bottom side Almeria on Sunday.