Campbell Stewart, Tyrese Kiesere, Toby Hull and Jesse Beeforth from the team presented their idea to the Waihoro (Cashmere-Spreydon) Community Board on March 30.
Board chairperson Karolin Potter said she "couldn't be keener" on basketball but was wary of the cost.
Setting up a half-sized court would cost a minimum of $45,000, she said. "It's a monster."
Another issue was that Cashmere Technical Football Club was using the park and would need to be moved for the construction of a court.
"We have to be respectful of the current users," said board member and city councillor Tim Scandrett.
Christchurch City Council head of parks, Andrew Rutledge, said the proposal would be considered if there was enough support from the community.
Basketball team member Toby Hull said the sport was "hugely popular" in Christchurch.