The England international completed a permanent move to Upton Park earlier in the summer after spending last season on loan from Liverpool, scoring seven league goals for the Hammers.
However, Carroll suffered a heel injury that has thrown his early season involvement into doubt, but McDonald is hopeful the 24-year-old can be ready in time for the Premier League curtain raiser.
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"The injury that he has is quite extensive and it takes time for the body to heal itself. He is doing everything he can to push on.
"He has been working really hard and there is still plenty of time for him to get himself fit for the start of the season."
McDonald has also revealed that West Ham still active in the transfer market and suggests two more players could be brought into the club before the start of the season.
He added: "The manager and the hierarchy are working very hard behind the scenes to strengthen the team even more.
"If we can bring one or two others in to give competition for places we will be in a really good place come August 17."