Monsanto disclosed the approach on Wednesday before Bayer confirmed its move, though neither released proposed terms.
The $42 billion market capitalization of Monsanto means that the deal would be likely to eclipse ChemChina's planned acquisition of Swiss agrichemicals company Syngenta -- a target Monsanto itself pursued last year -- and could face U.S. antitrust hurdles.
A Monsanto statement said that its board was reviewing the proposal, which is subject to due diligence, regulatory approvals and other conditions. There is no assurance that any transaction will take place, it added. Bayer shares dropped more than 8 percent to a 2-1/2 year low of 88.39 euros in early Thursday trading, with some investors worried by the potential cost of a deal.
Monsanto shares were seen 7.6 percent higher at $104.50 in pre-market trades.
UBS Global Asset Management, which Reuters data shows is among Bayer's 30 biggest investors, said it was "deeply concerned" about the burden on Bayer's finances from a takeover, saying it would prefer the companies to agree a joint venture or a nil-premium merger.
Deutsche Bank analysts said a deal could shift Bayer's center of gravity to agriculture, accounting for about 55 percent of core earnings, up from roughly 28 percent last year excluding the Covestro chemicals business Bayer plans to sell.
That would have a negative impact on sentiment among Bayer's healthcare-focused investor base, the bank said.
During World War II Bayer was part of I.G. Farben, the German chemical conglomerate that used slave labor and manufactured Xyklon B, used in the gas chambers during the Holocaust.