The tournament is uncertain due to travelling restrictions and health regulations amid COVID-19 pandemic.
Barclay's comment came after International Cricket Council (ICC) on Monday (July 20) said the tournament was still on schedule despite uncertainty amid the ongoing COVID-19 pandemic.
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In a media release, the governing body stated it will "continue to evaluate the situation in relation to being able to stage the ICC Women’s Cricket World Cup 2021 in New Zealand in February next year. In the meantime, planning for this event continues as scheduled".
"The decision (about the ODI World Cup) will be made in the next two weeks," Barclay told 'Radio New Zealand'. "Because if there is a need to postpone that event then obviously we need to know that sooner rather than later and likewise if it is to go ahead then we need to make a final decision so that we can throw all the resources necessary to run a first class world event in February."
Even though New Zealand has dealt with the health crisis admirably well and is among the least affected countries in the world, the Women's World Cup faces great logistical challenges, given the travelling restrictions and the necessary quarantine regulations.
"How do you get teams travelling around the world, they've got to hub through other countries and what are the implications of that?" asked Barclay.
"Then getting them through the quarantine restrictions that may be in place and of course all of that comes with a cost and so there are budgetary implications heading into February (but) all of that is surmountable," he added.
(Inputs from PTI)