The striker has been linked with a move away at the end of the season after reportedly growing frustrated with a lack of first-team opportunities since his return from Juventus last June.
Morata admitted this week that he missed the Juve dressing room and suggested he would have turned down the chance to return to the Santiago Bernabeu if there had not been a buy-back clause in his contract.
Zidane has confirmed that the Spain international will face Quique Sanchez Flores' side from the start and has assured him it will not be his only chance to impress across 90 minutes for the remainder of the season.
"I would not like it if Morata wanted to go at the end of the season," he told a news conference. "He's had fewer minutes, fewer than Karim, but he has had them. This is his home.
"He'll play from the start and it's not the last game in which he'll play from the start. But you can't stop that - there will always be players who have more minutes than others."
The champions' morale has taken a hit following their 4-0 Champions League thrashing by Paris Saint-Germain on Wednesday, but Zidane believes their European campaign will have no impact on the domestic title race.
"If Barcelona are knocked out, it won't change La Liga," he said. "We only look at what we do.
"In the defeat, we saw a very strong Paris Saint-Germain and a Barcelona who were less so. But there is always a return leg and you have to play. We know Barca are a very good team and they can still do things in the competition."
The former France star was hugely impressed by PSG's display but warned that they have a difficult task ahead of them if they want to go all the way in Europe's top competition for the first time.
"PSG are a clear candidate for the Champions League," he said. "They have great potential and they're among the favourites. But it's a long, hard road and it will be like that until the end. One result does not make you win the Champions League."