Cookson, who served as president of British Cycling from 1997 to 2013, said China had already seen some success in the sport but those results had come about more by accident than any grand plan.
Cookson pointed to Ji Cheng, who earlier this year became the first Chinese cyclist to race in, and complete, the Tour de France, as an example of China's potential.
"China has a great potential in cycling sport," China's official Xinhua news agency quoted Cookson as saying in Nanjing, which is hosting the Youth Olympic Games.
"I know there's young potential talents in China who have to be given opportunities and we already see some of them coming out almost by accident.
"If you can have one by accident, you can have two, but if you have a structure, you will have many more."
Britain topped the medal table in cycling at the last two Olympics, winning eight of 18 gold medals up for grabs at both the Beijing and London Games.
"To compete at Olympic level in any sport, it is not cheap," added Cookson. "China now is one of the biggest economies on the planet. If it chooses to do, it can invest more like we do and make success."
(Writing by Peter Rutherford in Seoul; Editing by Ian Ransom)
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