The attacking midfielder has been a reported target for West Ham's London neighbours Fulham in recent weeks, having been one of few consistent performers for the club so far this season.
McDonald does not expect Morrison to leave Upton Park before Friday's transfer deadline and is also hopeful manager Sam Allardyce can bolster the squad with new arrivals.
"As I say, there is lots of speculation about players. We'll see how things develop over the next 12 hours," he said on Friday.
"I would imagine Ravel will be staying until I'm told otherwise. He has been training and is a creative player who we will need."
West Ham have been linked with a host of players in recent weeks as Allardyce's men look to climb out of the Premier League relegation zone and preserve their top-flight status.
While he refused to be drawn on reported interest in Manchester City defender Joleon Lescott, McDonald backed Allardyce to add to the signings of Marco Borriello and Antonio Nocerino.
"Joleon Lescott is Manchester City's player and, until that changes, I cannot comment," he continued.
"It's all speculation. We're trying to improve and if we can get anybody else in, that would be a bonus.
"I wouldn't rule out anybody coming into the club.
"With it being deadline day, Sam is busy in the background trying to recruit players for us. We've recruited really well so far.
"We'll have a look at what our reports say and, if there is anything going, the manager is dealing with those enquiries."
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