Barbara Poma, an owner of the club, and Mayor Buddy Dyer spoke about the possibility a few weeks ago, Sara Brady, a spokeswoman for Poma told CNN.
In an interview aired Tuesday on WMFE radio, Dyer said, "We need to determine some period of time that we leave it exactly as is with some adequate fencing because there will be people ... that want to travel here to see it as it exists without making modifications."
Dyer imagined that period of time would be about a year and then the city would "transition to a permanent memorial."
Brady said Wednesday the discussions were preliminary.
A spokeswoman for the mayor said it is up to Poma on how to proceed and there is no rush to purchase the club, where 49 people were killed by a gunman June 12. More than 50 other people were wounded. The gunman was also killed.
Cassandra Lafser said if the city does buy the Pulse property it must go through a public process.
The nightclub was recently returned to Poma after being in police hands for weeks. Poma hasn't reopened the club, saying she was contemplating the future of the club. Before that, she had said she thought she would fix the damage to Pulse and reopen it at some point.
After someone broke in July 14, Poma called Pulse a "sacred place."
Since the days following the attack, the nightclub has a chain-link fence around it that visitors have decorated with flags, flowers, mementos and messages.
The city has announced other plans to ensure the dead aren't forgotten.
It plans a paver garden as one permanent memorial. The names of the victims will be on stones placed around Lake Beauty Park outside Orlando Regional Medical Center, where many of the wounded were treated.
The site was also home to 49 wooden crosses made by a carpenter from Illinois that were displayed outside the hospital. They are now in climate-controlled storage. The Orange County Regional History Center plans to use them and items from other temporary memorials at a permanent one, once a site has been determined.