Dish Network’s chances of buying DirecTV could be about as remote as a satellite that’s orbiting the earth.

That’s the take from sources close to Dish Chief Executive Charlie Ergen, who say that in addition to regulatory stumbling blocks the mercurial billionaire faces tough financial hurdles in acquiring his longtime rival.

Ergen appeared to get a fresh opening when activist investor Paul Singer’s Elliott Management took a $3.2 billion stake in AT&T earlier this month, prodding the telecom giant to sell off assets including DirecTV.

Singer’s team has spoken to Ergen’s team and is aware that Ergen would like to buy DirecTV, several sources close to the situation said.

Nevertheless, sources also noted that Ergen would have to reckon with the Department of Justice. For one, a merger would create the nation’s only major satellite-TV provider — a potential antitrust target.

Sources said DOJ antitrust chief Makan Delrahim would also likely be concerned that Dish is meanwhile in the middle of acquiring assets from T-Mobile as part of a deal to get the latter’s merger with Sprint cleared by US regulators.

Under the T-Mobile deal, Dish will be forced to spend between $10 billion and $15 billion to build a fourth major US wireless provider. To buy DirecTV, meanwhile, Dish would likely need to raise $10 billion in equity from buyout firms or other investors.

“There is not a long list of buyers for DirecTV,” a source said, adding that he believes private equity would not be interested in being minority partners in what would be a satellite behemoth.

The Wall Street Journal reported Wednesday that AT&T was exploring a sale of DirecTV, which is worth $25 billion based on a five times earnings before taxes purchase multiple.

On the positive side, a Dish-DirecTV merger could reap about $2 billion in synergies, JPMorgan analysts estimated in a Sept. 9 report. Presently, DirecTV has the biggest satellite market share with roughly 16 million subscribers. Dish, its closest satellite rival, has 9 million.

Nevertheless, a source close to Ergen said he could have a difficult time merging his business with DirecTV in an all-stock deal. That’s partly because Dish’s satellite business is valued at less than zero by Wall Street, which instead is banking on the marketability of its unused troves of wireless spectrum.

“A merger is too hard,” the source close to Ergen said.

Likewise, a possible move to spin off DirecTV to shareholders looks hard for AT&T, JPMorgan noted. It cited the “dis-synergies” of setting up a new, independent company that would be plagued by debt, falling revenue and dwindling subscribers.