Law enforcement sources tell TMZ ... a man in Altoona, Pennsylvania is being held for questioning in connection with last week's shooting in New York City.

Our sources tell TMZ ... local police responded after receiving a tip that the person of interest was seen in a McDonald's.

The man has a similar gun as the one used in the murder, the sources said.

The New York Times reports the person of interest had a written "manifesto" in his possession. The Times reports the detained man showed police the same fake I.D. used to rent the hostel room in NYC, where the murder suspect is believed to have stayed prior to last week's murder ... and the detainee was reportedly in possession of gun -- possibly a "ghost gun" -- and a silencer, according to law enforcement sources cited by the newspaper.

The gun used in the shooting has been the subject of speculation -- with some law enforcement sources saying the weapon is a veterinary gun commonly used on ranches and farms to put down animals, with a reduced-noise gunshot -- instead of a pistol fitted with a silencer, as was originally reported.

As we know ... an unidentified suspect walked up behind Thompson early Wednesday morning last week and fired multiple rounds outside the New York Hilton Midtown hotel, before calmly walking away. Police say the suspect walked into a nearby alley and rode a Citi Bike e-bicycle to Central Park, where he disappeared.

The suspect remains at large as police pursue multiple leads. Police have said the suspect is no longer in the city.

As TMZ has reported ... the suspect is believed to have traveled to Manhattan on a bus that originated in Atlanta that made several stops en route to the city. He stayed for several days prior to the shooting at a hostel in Manhattan, being photographed at the front desk in pics that have been widely distributed.

A new picture released this weekend shows the suspect looking directly into a camera inside a cab.

The backpack believed to have been worn by the killer was found Friday in Central Park -- inside the backpack, police found a jacket ... and fake Monopoly money from the board game.

Shell casings found at the scene of the shooting had the cryptic words "deny," "depose," and "defend" -- an apparent reference to a 2010 book titled "Delay, Deny, Defend," which slams the health insurance sector -- and, as we now know, Thompson was one of the industry's bigwigs.