If he gets the job, Mr Zhu will be in charge of implementing the ambitious privatisation plan for China's loss-making state-owned industries, as outlined by President Jiang Zemin at the opening of the 15th Communist Party Congress on Friday. It will be the toughest task yet for a politician who is widely admired as the most capable of China's top leaders, but whose forthright manner has earned him only grudging respect among some colleagues. Or as the official China Daily put it: "Even people who have been severely criticised by him admire him as a daring man."
"Zhu is bold and sweeping in the way he moves politically, but thereby he has had a real tendency to tread on entrenched interests and make bureaucratic enemies," said Professor David Shambaugh, a specialist in Chinese politics at George Washington University. "This is precisely the kind of prime minister China needs now, but will make for intense bureaucratic warfare and attempts to undercut his agenda."
Nicknamed "One Chop Zhu" when he was mayor of Shanghai in the late Eighties, he gained renown for decisiveness after slashing the jungle of red tapewhich threatened to strangle foreign investment in the city.
In 1992, already a deputy prime minister, he was catapulted into the top-level Standing Committee in charge of the economy. The following year, with inflation at 25 per cent in the cities and threatening to spiral out of control, Mr Zhu launched the savage austerity programme which earned him influential opponents, particularly among provincial party bosses whose freewheeling spending habits he attacked.
But the policy worked; inflation is now in the low single digits, economic growth is still strong, and Mr Zhu looks set to collect his reward. When the congress wraps up at the end of this week, it should become clear if he is the one who will succeed Li Peng as prime minister next March.
Mr Zhu will be very different from the present incumbent. He is a suave English-speaker, said to like literature and Chinese opera. Unlike most Chinese leaders, he is confident enough to speak off the cuff, looks visibly bored at party photo opportunities and on foreign visits is noticeably relaxed and spontaneous. According to the official biography, he "avoids accepting gifts, ribbon cutting and inscription writing."
Mr Zhu was born in 1928 in southern Hunan, the home province of Mao Zedong. He studied engineering at the prestigious Qinghua University, and joined the Communist Party in 1949, the year the People's Republic was established. In 1957 he fell foul of the party hardliners, after a three-minute speech criticising the system. During the Cultural Revolution he was sent to the countryside for five years and was not finally rehabilitated until 1979.
In the reform era of Deng Xiaoping, Mr Zhu soon proved himself at the State Economic Commission. In 1988 he was appointed mayor of Shanghai, and immediately pledged to boost the city's backward economy. He is also said to have told top tourism bureau officials that if Shanghai intended to become a world tourist destination they should first send workers out to clean the city's disgraceful public toilets.
Mr Jiang was Shanghai party secretary at this time and the two men, although not personally close, formed a solid working relationship. Immediately after the 1989 Tiananmen massacre, when Shanghai was in the grip of huge demonstrations, streets were barricaded and public transport ground to a halt, Mr Zhu went on television and managed to calm the situation by telling the city he had "never considered using troops or exercising any military control".
After the crisis, Mr Jiang was promoted to national party chief, and Mr Zhu took over as Shanghai party secretary. Even then, Shanghai was experimenting with converting its ailing state-owned firms into shareholding companies. In 1989, Mr Zhu said: "We can promote the best enterprises, let the best managers take senior positions in enterprises, and let the best workers have jobs" - ideas finally enshrined as policy by Mr Jiang last week.
If appointed as prime minister, Mr Zhu will be responsible for overseeing this policy at a national level and if it is successful there, it will transform the way China operates. But if it goes wrong, and Chinese workers take to the streets in protest, it will not only be Mr Zhu who loses his job.