McDonald allays West Ham injury fears
The trio did not feature as Sam Allardyce's men kicked off their pre-season programme with a 2-2 draw against League Two side Stevenage on Saturday.
However, McDonald insists their omission was merely a precaution and that he hoped they would be back in action later this week.
"We've had them in pre-season and they've been training but they just had little knocks or tightness, so we didn't want to take a chance and hopefully they'll be involved at Ipswich on Wednesday," he said.
"We went to Ipswich two pre-seasons ago and we got a bit of a thumping and that put everything into perspective.
"Hopefully, we will put in a good performance this time around ahead of our trip to New Zealand, where we'll also have two really good games."
Zarate signed for West Ham from Velez Sarsfield in May, while Carroll was a club-record £15 million acquisition from Liverpool in 2013.
Cole, meanwhile, is enjoying a second stint with the club having been briefly released last year.