Morata was pursued by Chelsea and Arsenal, among others, after Madrid exercised a buy-back clause to re-sign him from Juventus for €30 million ($33M).
Morata's agents met with Madrid on Thursday and a €60 million ($66M) bid was turned down. An improved €80 million offer from an unnamed club was dismissed Monday after another meeting.
It was expected that the European champions would immediately sell the 23-year-old for a profit upon his return, but Florentino Perez and Zinedine Zidane have pushed to persuade him he has a future in Madrid.
Zidane and Perez are both fans of Morata and played a significant role in assuring the Spain international that he will be handed a fair shot at breaking into the starting XI next season.
Morata and his representatives were also said to be encouraged by Zidane's selection of the likes of Lucas Vasquez on the basis of their good form over big-money signings such as James Rodriguez.
The striker will compete directly with Karim Benzema for the center forward role between star wingers Gareth Bale and Cristiano Ronaldo.