According to Diario Gol, Sky Blues boss Pep Guardiola has named the duo as his top summer transfer targets.
Isco, who was recently linked with Manchester United, has struggled to hold down regular first-team football at Real this season and is said to be keen on a move elsewhere.
The report goes on to suggest that Kane could be tempted by a move to the Etihad Stadium if City sign Isco, with the England international said to be eager to play alongside the Spaniard.
Kane has repeatedly been linked with Real, but would allegedly be willing to snub the La Liga giants if City lodge a big-money bid for him this summer.
Spurs, however, have been unwilling to listen to offers for their top goalscorer.