Argentina Cops Are Searching for Liam Payne's Missing Rolex Watch

9:53 AM PT -- Law enforcement sources in Buenos Aires confirm to TMZ ... Liam Payne's father, Geoff, asked for the missing Rolex watch after he was given Liam's possessions when he flew to the city last month, saying the watch has sentimental value. Police confirmed the Rolex has disappeared.

Security camera video reportedly shows the watch on Liam's wrist hours before he died -- but authorities say Liam was not wearing the watch when he fell from the balcony, and they officially state it was not stolen after he fell.

Police in Argentina are trying to locate Liam Payne's Rolex watch after his drug-fueled fatal fall from the third-floor balcony of his hotel room, TMZ has confirmed.

Law enforcement sources tell us ... the former "One Direction" singer's expensive timepiece went missing around the time his body landed in the courtyard of the CasaSur Palermo Hotel in Buenos Aires on October 16.

La Nacion, a Buenos Aires newspaper, reported the watch was not found during police raids on the hotel and the homes of 3 suspects who were arrested last week in connection with Liam's death.

The defendants -- a friend of Liam's, a hotel housekeeper, and an alleged drug dealer -- were charged respectively with abandoning the musician and supplying him with narcotics.

The media outlet says police plan to return to the hotel for another search of Liam's suite in case they missed the watch during their initial sweep.

La Nacion also claims surveillance footage shows Liam wearing the watch the day he died, quoting a prosecution source who said ... “He had it in one of his hands and he had it at least two to three hours before his fatal hotel fall."

The cops have another mystery to solve in the ongoing case.