BBC Sport's David Ornstein reported as much on Sunday:
Per the Telegraph's Matt Law, Bale had been nearing a move that would have seen him earn more than £1 million per week.
According to John Percy of the same outlet, Real president Florentino Perez won't let Bale go without receiving a transfer fee from Suning, who have until Wednesday before the Chinese transfer window closes.
Foreign signings in the CSL are subject to a 100 per cent levy, effectively doubling the cost of overseas players for Chinese clubs.
Bale has three years remaining on his contract with Real Madrid.
Per Ornstein, Los Blancos boss Zinedine Zidane said the Welshman leaving the club would be "best for everyone."
Bale's agent Jonathan Barnett responded to those comments by telling ESPN FC that Zidane is a "disgrace."
He also told Le Journal du Dimanche (h/t Eleven Sports) that the Frenchman "doesn't like Gareth Bale. There is no relationship between them, there never has been."
However, given that very few clubs have the resources to fund a move for the winger, if his move to China is off, he may well remain at the Santiago Bernabeu this summer.
The 30-year-old has contributed a great deal in the Spanish capital during his six years at the club:
Football writer Andrew Gaffney thinks keeping him would be worthwhile for Los Blancos:
Bale's future looked under threat from the moment Zidane returned to the club in March, and his days appeared to be numbered when the manager left him out of the final three matches of the campaign.
The player can still have a big impact for Real next season, but he and Zidane will need to mend their relationship for that to happen.
According to Law, Bale earns £600,000 per week in Madrid, so the club can ill afford to have him sat on the bench or up in the stands when he's fit to play.