The 21-year-old Spain international has scored eight goals in 35 Primera Division appearances so far this season, and is also believed to have attracted interest from Manchester City and Paris St Germain.
Isco signed a new contract with Malaga in January to keep him at the club until 2016 but has a buy-out clause of 35million euros (£30million).
Malaga director Francisco Aguilar told Spanish newspaper Marca that Real are keen on Isco, but a deal is still a long way from being confirmed.
"Real Madrid are interested in signing Isco, but nothing is official yet," Aguilar said.
"It fills us with pride that a lad who has come through at Malaga has become the player that he is now.
"If he leaves Malaga it will be to a big club and it will be to the benefit of the coffers at Malaga. Clubs that want him will have to meet his buy-out clause."