The Spaniard has followed up a stellar season with Malaga as they reached the Champions League quarter-finals with a starring role as the Spanish under-21 side reached the final of the European Championships in Israel.
Asked if he already had received offers from City and Madrid, the 21-year-old, whose full name is Francisco Román Alarcón Suárez but who who goes by the name of Isco admitted he had.
"They are on the table, yes," he was quoted as saying by Spanish sports daily AS.
"They are the two propositions on the table. I hope to decide soon because I still have a contract with Malaga.
"I know that both Manchester City and Real Madrid are great clubs. I want that whatever happens will be the best for me and for Malaga."
City finally confirmed last week that Isco's old boss at Malaga, Manuel Pellegrini, had been appointed as the club's new manager.
However, despite recently describing the Chilean coach as his "footballing father", Isco claimed that Pellegrini's arrival in Manchester would not be a decisive factor in where he moves.
"It is true that I already know Pellegrini, I know how he works and he has been fundamental in my career in the two years I have been at Malaga with him," he added.
"It is a point in favour that we have already been together and I know how he works but it is not definitive."
A decision could even be made this week with the player's commitments with the under-21 side due to finish after Tuesday's final against Italy.
Isco scored 12 goals in all competitions for Malaga last season as "Los Boquerones" finished sixth.
But they have been banned from taking part in next season's Europa League because of a one-season UEFA ban for not paying debts owed to employees, other clubs and tax authorities on time.