Morata has frequently been linked with a move away from the Bernabeu and although a transfer to Manchester United failed to materialise, Chelsea appeared favourites to sign the Spanish international ahead of next season.
However, according to Onda Cero, the 24-year-old has received a lucrative offer from Tianjin Quanjian to make the switch to China.
It has been suggested that a proposal of £500,000 per week is on the table on a contract which would last until 2022, leaving Morata with a decision to make over his future.
Last season, Morata scored 20 goals in all competitions but he was only used as backup by Zinedine Zidane, with as many as 24 appearances coming from the bench.
Morata still has four years remaining on his existing deal at the Champions League holders.