The All England Lawn Tennis Club (AELTC) has made a 63.75 million pound ($83.8 million) offer, according to British media reports, to buy out early the lease of neighbouring Wimbledon Park Golf Club.
Wimbledon already owns the site but it does not revert to them until 2041.
"We have a fantastic site but we would like to create a bigger site," Mick Desmond, the AELTC's commercial and media director, told reporters at the Leaders Sports Business Summit at Chelsea's Stamford Bridge ground.
"We believe we would become a much bigger, more prestigious event by getting that land but also giving something back to the community.
"There's a constitutional vote today. So effectively they have to change their constitution in order to then vote on the bid that's in front of them. We obviously think it's a very fair bid," he added.
The move would add 73 acres (295,421 square metres) to the 42 acres currently used to host one of the pillars of the tennis calendar.
The land could be used to build courts for qualifying matches.
"We're going to get it anyway," said Desmond. "In 2041 it's going to come to us naturally because that's when the lease runs out. "So for us, it's really buying a 20-year window."
Desmond said the AELTC kept a close eye on the expansion plans of other grand slams, notably the U.S. Open and France's Roland Garros, as well as other major sporting events.
"We think this would be fantastic for the UK," he said.
"We set ourselves ambitions of always trying to raise the bar and I think we can do so much within our current configuration and we can go much further by having a broader configuration.
"If the bid's not accepted, then there are clear plans of what still needs to be done on the current site. But it may well change some of the configuration and some of the thinking around that," he added.