"We see this proposed offer as an attractive transaction that is likely to proceed at or relatively close to this price level, especially given Murdock's strong ownership position, CEO role, and apparently strong personal liquidity position," Jonathan Feeney of Janney Capital markets said.
Murdock, who is also Dole's chairman as well as its biggest shareholder with a 40 percent stake, returned as CEO in February after David DeLorenzo left to run two businesses sold by Dole to Japan's Itochu Corp.
Murdock is a high school dropout who ran the company as CEO from 1985 until 2007. As chairman he took Dole Foods public in 2009.
The nonagenarian has said he wants to live to be 125, pinning his hopes on a strict diet, daily exercise and a lifestyle free of pills or supplements, according to his Forbes profile.
The bid comes after Dole sold its packaged foods and Asia fresh produce businesses to Itochu last year for $1.7 billion, paring its size by a third.
The company is now left with its fruit and fresh vegetables business in North America and its fruit businesses in Latin America, Europe and Africa.
Dole, like rival Chiquita Brands, has been struggling with volatile demand and low prices for bananas, its biggest-selling product.
The company, which traces its roots to pineapple plantations set up in Hawaii in mid-1800s, said it would establish a special committee of independent directors to consider the proposal.
The offer has an enterprise value of $1.5 billion, Murdock said in a statement on Tuesday.
It represents a premium of about 18 percent to the stock's close on Monday. The company's shares were trading at $12.38 Tuesday morning on the New York Stock Exchange.
Prior to the bid, the stock had fallen 32.7 percent since touching a life-high of $15.16 in September, when it struck the deal with Itochu.
Murdock said Deutsche Bank would advise on the transaction and that he had received a "highly confident" letter from the lender on the financing for the deal.