Given the size of the deal, CAF is seeking a partner to buy the unit, the newspaper reported.
The train signalling arm is a crucial technology business that allows railways operators to increase the number of trains circulating on rail lines and includes driverless train technology.
A CAF spokesman declined to comment and no one was immediately available at Thales for comment.
($1 = 0.8210 euros)
(Reporting by Inti Landauro, Matthieu Protard and Michael Susi; Editing by Alex Richardson)