He said the idea of a pop-up theatre came to him while reading a bedtime story to his now 5-year-old daughter, Nancy, about three years ago.
"We were reading a pop-up book and one of the pop-ups was Shakespeare's Globe theatre. She said: 'Daddy, can we go out to that?'
"I said: 'Well, actually, we can't.' So I thought afterwards: 'Wouldn't it be great to bring the theatre here?'"
The current Globe in London, built in 1997, is based on the original theatre built in the 16th century which was home to many of Shakespeare's plays.
An exact location for the temporary building has not yet been confirmed, although plans are already in place involving the Auckland Council and a local building company.
Dr Gregory said the construction of the replica - estimated to start later this year - would cost about $450,000 and money for it would come from various avenues including ticket sales, state funding and sponsorship.
Plans to involve local artists are also in the works, with Shakespeare's A Midsummer Night's Dream, performed entirely in te reo, set to go on stage in February. That play is being written by Kiwi actress and director Rachel House.
A project inviting thousands of drama teachers is also in the mix and there are plans for schools to see performances at the site as well.
"It's a project that's really exciting and something new for not only Auckland but New Zealand," Dr Gregory said.
"Seeing Shakespeare's plays performed in the environment they were written for is a unique experience - as much a party as a performance."
Auckland's pop-up Globe theatre
• Full-size replica of London's famous Globe theatre.
• Original Globe theatre was built in the 16th century and was home to many of William Shakespeare's famed plays.
• Pop-up Globe set to open in Auckland early next year.
• Estimated to cost about $450,000 to construct.