Plans for the 9.4-hectare park were on Wednesday unveiled by the All England Lawn Tennis Club, and include details of a third show court.
The proposals are part of the club’s purchase of the neighbouring Wimbledon Park Golf Club.
They will see the private land transformed into a year-round public park with 1,500 new trees and a restored park lake.
It would be the first public space to open in the capital since the Queen Elizabeth Olympic Park in Stratford.
With a capacity of 8,000 spectators, the Parkland Show Court would be the third biggest after centre court, which has a capacity of 14,979, and no 1 court, which holds 12,345.
The plans also include details of 39 new courts which would be used for the Wimbledon qualifying rounds, rather than the club’s site in nearby Roehampton, and player practice during the competition.
But they have been met with resistance from local residents, who say the particular landscaping of the original golf club by Capability Brown must be maintained.