The report surveyed 600 employers about their hiring intentions. It suggests businesses are more worried about shortages of drivers than any other role.
About one-in-five (21%) employers looking to hire permanent drivers and distribution workers and 23% of employers looking for drivers via agencies predict shortages throughout November and December.
REC chief executive Kevin Green told HR magazine the rise of online shopping has put increased strain on companies' recruitment processes around Christmas.
"With an ageing demographic and it being expensive to train lorry drivers up to the necessary qualifications, drivers are turning out to be very hard to come by," he said.
Elsewhere wider skills shortages continue to affect UK companies. Almost nine-in-10 (89%) companies intend to increase their permanent headcount over the next three months, although 65% are having to use temporary staff to plug skills gaps.
Green called on the government to revisit its immigration policies to aid employers looking for high-skilled workers.
"We want government to be supportive of people coming into this country, either to study or to work," he added.
