Rep. Adam B. Schiff (Calif.) is set to chair the House Intelligence Committee once Democrats take control in January. (Susan Walsh/AP)

To the long list of investigations House Democrats have planned for next year, add a look into whether President Trump used his office to try to punish companies associated with CNN and The Washington Post.

Incoming Intelligence Committee Chairman Adam B. Schiff (D-Calif.) brought up the potential probe during an interview with Axios as an example of the type of oversight Democrats should be exercising.

Schiff pointed to Trump’s effort to block AT&T from purchasing Time Warner, the parent company of CNN, and his desire to get the U.S. Postal Service to increase shipping costs on Amazon, whose chief executive, Jeffrey P. Bezos, also owns The Post.

“The president is not only castigating the press but might be secretly using instruments of state power to punish them,” Schiff said in an interview with The Post on Sunday. “That’s a great threat to press freedom.”

The threat of investigation comes after the White House revoked CNN reporter Jim Acosta’s press pass last week, which was seen as an escalation of Trump’s conflict with the media.

Such an investigation would not go through Schiff’s committee, but probably the Oversight or Judiciary panels. He said Democrats are convening this week, and he intends to raise it as a priority with his colleagues.

“I hold it up because it’s such a clear example of the vital oversight that’s been missing to make sure the president is not abusing his power,” Schiff said.

Trump complained that the AT&T and Time Warner merger was a consolidation of too much power. And he has claimed Amazon is ripping off the U.S. Postal Service by paying low rates.

An investigation into whether Trump’s attempt to block AT&T’s acquisition of Time Warner over the summer or whether his personal call on the postmaster general to double Amazon’s rates in May were inspired by his fights with the media will have to compete with dozens of other pressing oversight matters.

The Judiciary Committee will focus immediately on acting attorney general Matthew G. Whitaker’s potential conflict of interests in overseeing the special counsel’s Russia investigation, while the Oversight Committee has a long list, including allegations that Trump violated the Constitution’s emoluments clause forbidding a president from taking money from foreign governments.

In his role, Schiff said he plans to pick up the Russia investigation where House Republicans left off. Whether or not special counsel Robert S. Mueller III has wrapped up his report by January, when Democrats assume power, Schiff said, there will be important work for his committee on the issue.

“We never walked away from it,” Schiff said of his chamber’s inquiry into Russian interference in the 2016 election. “That will be our intention, to finish this work, and we’ll now have the power to compel people to testify.”