The La Liga giants experienced a low-key summer window after failing to sign Kylian Mbappe despite a prolonged transfer saga that ended with him joining Paris Saint-Germain. Los Blancos have made noted efforts to change their transfer policy in recent years, looking to sign promising young players they can ease into the first-team with Marco Asensio a prime example of its current success.
The club provided another demonstration of that during the summer, paying £38m to secure the services of 16-year-old Brazilian sensation Vinicius Jnr having also recruited 19-year-old Theo Hernandez and 21-year-old Dani Ceballos.
Real are looking to continue that trend of buying young talent, but also want someone with a superstar profile; the sort of signing that has come to define the club over the last two decades.
Marca now report Kane and Alli are among a list of players now on the club's radar.
Kane in particular has been the subject of transfer speculation linking him with a £200m move to the Santiago Bernabeu, admitting this week he would never rule out a move to Spain.
"I think in football, you never know and you never rule out anything. It is not something that I definitely want to do but it could happen. You just never know.
"Like you said, at the moment, I am very happy where I am here [Tottenham] – that is all that matters," Kane, who has scored 11 goals in nine appearances this season. "We will see what happens, but for now that is all I am focusing on."
Real have not made a true 'Galactico' signing since bringing James Rodriguez to the club following his wonderful World Cup campaign with Colombia in 2014. A year before that they paid a world record transfer fee to sign Gareth Bale from Spurs but since then that record has been broken three times with the transfers of Paul Pogba, Ousmane Dembele and Neymar.