The 25-year-old has attracted the attention of several European clubs so far during the transfer window, including that of Manchester United and West Ham United.
Zidane has given little indication that the attacker will be allowed to leave but was upfront about the player's situation at the club.
"The idea with James is the same as with everyone else - he's a Real Madrid player," Zidane told reporters.
"I'm not going to tell you that James is a starter. He's an important player. We'll see what happens this year, I have a big squad and it's complicated."
The Real manager also hinted that James' challenge to find a regular starting spot is likely to be shared by Alvaro Morata.
Morata's buyback clause was activated by Real earlier in July, bringing the Spain international striker back to the Bernabeu from Serie A champions Juventus.
"He [Morata] is one more player in the team," Zidane added. "He knows what Madrid is and we're happy to see Alvaro with us.
"We're going to have a much bigger squad and everyone will be important. He'll be one more," the 1998 Ballon d'Or winner concluded.