The elite law firm Skadden, Arps, Slate, Meagher & Flom has had discussions with President Trump’s advisers about a deal to avert the type of executive order that the White House has been imposing on many of its competitors, according to five people briefed on the matter who were not authorized to speak publicly about private conversations.

The talks represent an extraordinary turn in Mr. Trump’s campaign against law firms and the legal system more broadly, marking what appears to be the first time that a major firm has tried to cut a deal with the president before he could issue an executive order. Recent orders targeting other law firms have restricted the work they can do with the federal government.

The Skadden discussions are also the latest example of how large law firms, afraid of a protracted battle with Mr. Trump, are eager to strike deals.

The White House has signaled that more firms are in the president’s sights to receive executive orders, particularly those that employ lawyers who have worked on investigations into Mr. Trump or on causes that his supporters object to.

Two of the people briefed on the matter said that Skadden was not the only firm in discussions with Mr. Trump’s team, and that multiple deals could be announced in the coming days.

It is unclear how the talks got started or whether Skadden will ultimately reach an agreement with Mr. Trump. But on Wednesday, Mr. Trump hinted that such deals might emerge and boasted about his track record of bringing big law firms to heel.