The 21-year-old has been kept on the fringes of the first team fold at Santiago Bernabeu since linking up with Real earlier this year.
His potential has impressed the Primera Liga giants, though, and they are weighing up the merits of a full-time deal.
No talks have been held as yet, but Casemiro's representative is expecting discussions to take place.
Joseph Lee told Estado de S. Paulo: "It's certain that Real Madrid will want to keep the player, but they need to reach an agreement with Sau Paulo first."
Sau Paulo are reluctant to discuss a possible summer move, with there nothing to report on the transfer front.
Vice-president Joao Paulo de Jesus Lopes said: "It's premature to talk about this. They haven't contacted us yet and there is a confidentiality clause."