The company's Hong Kong-listed shares rose more than 70% at one point before closing almost 18% higher.
However, Glencore denied knowing any specific reasons for the wild swings in a statement to the Hong Kong stock exchange.
The agricultural unit could be worth $10bn (Â£6.6bn), according to reports.
"The board confirms that it is not aware of any reasons for these price and volume movements or of any information which must be announced to avoid a false market in the company's securities," Glencore said.
The Reuters news agency reported last week that Glencore was in talks with a Saudi Arabian sovereign wealth fund and China's state-backed grain trader COFCO, as well as Canadian pension funds, to sell a stake in its agricultural business.
Singapore's sovereign wealth fund and Japanese trading house Mitsui were other potential buyers, Bloomberg reported.
Despite the rise to 109.2p in afternoon trading in London, Glencore's shares were still down by two thirds compared with the same time last year.
Its share price experienced big fluctuations last week on fears that the dramatic falls in commodity prices in recent months would affect its ability to keep paying its debts.
The company must service the $30bn debt mountain created by its ambitious 2013 takeover of Xstrata. That deal added dozens of mines in numerous countries to the commodity trader's business.
Paul Gait, analyst at Bernstein Investment Research, said that Glencore had become the "poster child for the mining industry in aggregate".
However, he said some investors realised that the company was not facing a "Lehman moment" because its assets well exceeded its liabilities.
Bernstein held its "outperform" rating on the stock with a target price of 450p.
Meanwhile, chief executive Ivan Glasenberg called on other mining companies to close loss-making copper mines following the slide in copper prices.
"Don't create oversupply in the market for no reason," he said at a Financial Times conference in London on Monday.
Glencore had stopped output at two copper mines in Africa, Mr Glasenberg said.
Shares in embattled mining giant Glencore have jumped 17% following reports it was in talks to sell its agriculture business.