Federal prosecutors in Manhattan are investigating whether Michael Cohen, the longtime personal lawyer for Donald Trump, illegally engaged in secret lobbying, people familiar with the investigation said, as part of the government’s broader probe into Mr. Cohen’s business dealings.

In the course of that investigation, the prosecutors have contacted companies that hired Mr. Cohen as a consultant after Mr. Trump won the 2016 presidential election, including AT&T Inc. and Novartis AG , according to other people familiar with the matter. The companies paid a total of about $1.8 million to Mr. Cohen in 2017 and early 2018 for his insights into the Trump administration.

Investigators in the U.S. attorney’s office for the Southern District of New York are examining whether Mr. Cohen violated any federal disclosure laws in connection with his consulting deals, including whether he lobbied for domestic or foreign clients without properly registering, the people familiar with the investigation said.

Federal prosecutors in New York have been investigating Mr. Cohen for bank fraud, campaign-finance violations and other possible crimes, The Wall Street Journal has previously reported. Mr. Cohen hasn’t been charged with any crime, but the array of possible charges against Mr. Cohen could put additional pressure on him to cooperate with prosecutors, according to defense lawyers.

Mr. Cohen has previously denied any wrongdoing. Neither he nor his lawyer, Stephen Ryan, responded to a request for comment.