The Korean circuit's current contract, agreed before Park arrived, runs to 2016 with an option to extend for five years.
The race has ended substantially in the red every year, according to local media reports, with an operating loss of about $37 million in 2012.
"We certainly wish to improve the contract so that we can continue the event with the support of provincial parliament and the central parliament and public opinion," said Park.
The race has become a talking point for low attendances, with many more empty seats than spectators both days. although Park put the overall figure at 160,000.
Drivers, used to being mobbed by fans and autograph hunters at circuits like Monza and Monaco, experienced a quieter weekend for a change.
"You just have to try to draw inspiration from the empty seats," said Mercedes' Lewis Hamilton witha wry grin.
His compatriot and former teammate, Jenson Button, spoke enthusiastically of the food, the scenery and the lack of anything to distract from driving.
But he also missed the buzz of a cheering crowd.
"It's always sad when there are no fans at a race," the 2009 world champion said. "It hasn't really got the South Koreans excited and they don't travel to see the race.
"If you have a full house it makes the atmosphere and makes it a special race.
"This place doesn't have that because no one comes to watch it."
Asked whether he would miss the race if it disappeared from the calendar, Button's hesitation spoke volumes.
"I don't know what to say to that one," he finally said.
(China Daily 10/09/2013 page23)
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