By Cara Lombardo, Maureen Farrell and Dana Cimilluca

NextEra Energy Inc. recently made a takeover approach to Duke Energy Corp., according to people familiar with the matter, testing the waters for what would be a $60 billion-plus combination of two Southern utilities.

Duke rebuffed the approach but NextEra is still interested in pursuing a deal, some of the people said. There is no guarantee NextEra will do so and if it does, that a deal would result.

Should there be one, it would be big. Duke, based in Charlotte, N.C., has a market value of roughly $61 billion following a 14% decline in its share price this year, and an acquisition of the company could be the largest utility deal ever and the biggest merger so far this year.

Pulling one off won't be easy. First, NextEra would have to overcome any resistance from Duke and its executives, and hostile deals in the utility industry are rare. Any agreed deal would have to pass muster with an array of government officials in a highly regulated industry.

With a market value of about $139 billion after its stock rose 22% so far this year, Juno Beach, Fla.-based NextEra is the largest public utility company in the U.S.

It owns Florida Power & Light Co., which has more than 5 million customers in Florida and is the biggest rate-regulated electric utility in the U.S. by retail electricity produced, according to the company's website. It also owns Gulf Power Co., which serves more than 470,000 customers in eight counties in northwest Florida.

Utility investors see Florida as a particularly desirable market given the constant need for air conditioning and growing population.

NextEra also owns a clean-energy business that, along with affiliates, is the world's largest generator of renewable wind and solar energy. It also operates emissions-free electricity from plants in Florida, New Hampshire, Iowa and Wisconsin.

Duke provides electricity to roughly 7.7 million retail customers in six states, including the Carolinas, some Midwestern states and Florida, according to its website, and distributes natural gas to more than 1.6 million customers in Ohio, Kentucky, Tennessee and the Carolinas. It has a commercial business with power-generation assets in North America including a renewables portfolio.

NextEra has been an active acquirer of smaller assets in recent years and has also eyed larger deals, benefiting from its bulk and a stock price that has outperformed those of its peers. It announced a deal Tuesday to buy an independent transmission company for $660 million, including debt.

NextEra, run by James Robo, became a renewable energy goliath using tax subsidies to help finance wind and solar projects around the country and avoiding debt. It sells the output to utilities, many of which must procure power from green sources to meet state mandates. It went from being the 30th largest U.S. power company in 2001 to the largest today. But it has faced challenges in trying to expand, including regulatory pushback and the phasing out of certain tax credits. Texas regulators rejected its bid in 2017 to buy a large transmission company and Hawaii regulators rejected its bid for the state's largest utility in 2016.

Duke is run by Lynn Good and founded in 1904. It grew through a series of deals, including a roughly $5 billion deal, excluding debt, to buy Piedmont Natural Gas Co. that closed in 2016.

Since the coronavirus pandemic kept many people out of offices and working from home since mid-March, utility companies have been dealing with a surge in retail energy use -- as big chunks of the population work from home -- and a decrease in commercial demand. Duke, for example, said in its second quarter that commercial and industrial customer electricity volumes fell 13% and 15%, respectively, though most of its larger business clients have resumed operations. While retail use typically offers higher profit margins, it isn't clear how long large portions of the population will continue its outsize use as workers are expected to gradually return to their offices.

A handful of other utility companies have recently flirted with deal making, sometimes at the behest of activist investors. Evergy Inc., a roughly $11 billion electric utility based in Kansas City, Mo., was urged by Elliott Management Corp. to consider selling itself. Evergy undertook a strategic review but didn't ultimately pursue a sale. Its chief executive officer announced plans to retire in August.

CenterPoint Energy Inc., where Elliott has also been involved, in May formed a strategic review committee that plans to make recommendations to the board by October. The company has said it will update investors by early next year.

The biggest deal announced so far this year is Nvidia Corp.'s $40 billion acquisition of SoftBank Group Corp.-owned chip designer Arm Ltd. Merger and acquisition volumes are down 22% globally and 43% in the U.S. compared with last year, in large part because executives shifted focus from deal-making to respond to the impact of the coronavirus pandemic. Recently, however, the M&A market has begun to show signs of life as companies begin to regain their footing and look to establish strategic plans for the post-pandemic era.

Write to Cara Lombardo at cara.lombardo@wsj.com, Maureen Farrell at maureen.farrell@wsj.com and Dana Cimilluca at dana.cimilluca@wsj.com