Spanish reports in Punto Pelota claim that the defending La Liga champions are torn between the two summer transfer targets - with a move for City's Aguero thought to be achievable at €45m.
Aguero came close to a Real Madrid switch two years ago, but the then-Atletico Madrid striker eventually opted to join Manchester City. Still, he remains a transfer target for Jose Mourinho's side, and could displace one of Gonzalo Higuain or Karim Benzema from the first-team squad.
But Real Madrid's Zinedine Zidane is thought to be pushing hard for Spurs star Gareth Bale, and the report claims there's a faction within the Bernabeu that feel Bale would be the bigger catch.
The Tottenham star would likely battle with Angel Di Maria for a starting spot, and Real Madrid would like Bale to make a telling impact similar to the emergence of Raphael Varane this season.
Di Maria may even become expendable, with Manchester United thought to be interested in the Argentine winger.
Real Madrid look set to cede their La Liga title to Barcelona this season, with Tito Vilanova's side comfortably clear atop the table.
Speculation has raged over the future of Bernabeu boss Jose Mourinho, and the club's transfer strategy could remain uncertain until the future of the Portuguese manager is sorted.