In a bid to create a global seeds and pesticides giant, Bayer is now offering $65 billion for Monsanto, or $127.50 a share.
The German company said it was in advanced talks with Monsanto, but warned there was no guarantee a deal would result.
Bayer’s initial offer of $122 a share in May was rejected by Monsanto for being “financially inadequate”.
The record all-cash offer valued the American company at $62 billion.
In July, Bayer raised its offer to $125 a share, but was again rebuffed.
Bayer and Monsanto combined would create the world’s biggest agricultural supplier and be a market leader in the US, Europe and Asia.
The German company produces seeds as well as chemicals to combat weeds and insects, but it is better known for its healthcare products such as Aspirin and Alka-Seltzer.
The American company is primarily known for its genetically modified seeds for crops including corn, soybeans, cotton, wheat and sugar cane. Such seeds have attracted criticism from some environmental activists.
The higher offer comes amid a wave of mergers in the agriculture sector.
Rivals including Dow Chemical, DuPont and Syngenta have all announced tie-ups recently, although some have yet to be cleared by regulators.
The drop in commodity prices has put pressure on companies such as Monsanto, with farmers’ cutting orders for supplies.
However, a Bayer takeover of Monsanto could raise US competition concerns because of the sheer size of the combined company and the control it would have over the global seeds and sprays markets.
Farming groups have raised concerns that such mergers could lead to fewer choices and higher prices.
Insiders said that although the two companies were close to reaching an agreement on price, they had yet to agree on a strategy on how to deal with potential regulatory hurdles.
Bayer shares have fallen by close to a fifth this year and ended at €94.24 on September 5, valuing the company at €78 billion.
Monsanto has risen 9% since the start of the year and closed on September 2 at $107.44, making it worth just over $47 billion. Wall Street was closed on September 5 for the Labor Day holiday.
German chemicals giant Bayer has made a $62 billion offer for American multinational agrochemical and agricultural biotechnology corporation Monsanto, in a deal that would create the world’s biggest agricultural supplier.
Both companies confirmed last week that Bayer had launched an offer for the US seeds giant.
Monsanto is primarily known for genetically modified crops, often leading to vocal activist criticism.
The offer comes amid a wave of mergers in the industry.
Rivals DuPont, Dow Chemical, and Syngenta have all announced tie-ups recently, although they have yet to be cleared by regulators.
Bayer said the offer of $122 per share represented a 37% premium on the price of Monsanto shares before rumors about the takeover bid emerged in the media.
When news about the takeover offer broke last week, Bayer shares took an 8% hit and a number of large Bayer investors voiced their criticism of the prospective deal.
Bayer has a market value of about $90 billion, making it the second-largest producer of crop chemicals after Syngenta.
Monsanto, which has a market capitalization of $42 billion, attempted to buy Swiss rival Syngenta in 2015.
However, Syngenta ended up accepting a $43 billion offer from ChemChina in February, although that deal is still being reviewed by regulators in the US.
Bayer’s acquisition of Monsanto is expected to be bigger in value than the ChemChina-Syngenta deal.
The biggest merger in the chemicals industry took place late last year when Dow Chemical teamed up with Du Pont to form a new $130 billion company.