It is understood that this is due to various factors, including the implications that a move for the Brazilian would have on future pursuit of his team-mate, Kylian Mbappe.
Madrid has been keen to explore the possibility of signing Neymar, after it emerged he wanted to leave France.
But he is no longer a target, especially with his desire to rejoin their LaLiga rivals Barcelona.
Zinedine Zidane’s side is instead focusing their attention on other targets, such as Manchester United midfielder Paul Pogba.
Real are also aware that bringing in Neymar at this stage, may prevent them from returning to the French capital to buy Mbappe.
Mbappe is considered to be a more suitable option at just 20 years of age, with Madrid likely to push hard to sign him in the future.
