"Just to be absolutely clear, because I know there's this talk going around...I'm not the man for PM, I say that categorically. It's not me," the 59-year-old leader was quoted as saying by the local media.
"I know myself, I know what I can do and it's not me. I'm good at policy-making, good at advising my younger colleagues and supporting the PM, not being the PM. That's not my ambition and that's not me," he said.
Tharman is second Deputy Prime Minister in the cabinet and serves as chairman of the Monetary Authority of Singapore, the de-facto central bank.
Prime Minister Lee, 64, took ill on August 21 while delivering a National Day Rally speech. He was treated for prostate cancer in February last year.
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Singapore's ruling People's Action Party since independence is grooming younger generation leaders for the next parliamentary general election due in January 2021.
Meanwhile, Tharman said Singapore is in for a tough economic period during the second half of this year.
"This year we had soft (economic) growth in the first half of the year, I think the second half of the year will be weaker, so we will probably end up somewhere in the lower end of the 1-2 per cent range (of the GDP)."
"Structurally, we're now in a new mode of growing. We can't keep growing by increasing manpower, we have to get productivity up.
"But even if things go well in Singapore, structurally we're talking about normal growth being 2-3 per cent, which is relatively good by the standards of most economies," he said.
Singapore recorded 2 per cent economic growth last year.