EXCLUSIVE

USC football player Josh Shaw was named in a burglary report ... stemming from an incident that went down Saturday night ... law enforcement sources tell TMZ Sports.

We're told Shaw was NOT named as a suspect in the burglary.

Here's the breakdown -- we're told someone called police to report a suspicious person "shimmying" down the side of a building in downtown L.A. near the USC campus. The tipster gave a description of the suspicious person to police.

We're told cops went to the building to investigate -- and spoke to a woman who lived in the building. Cops gave the woman the description of the suspicious person and asked if she had seen anyone who matched the description.

We're told the woman said, "Yes, that sounds like my boyfriend Josh Shaw."

Cops took a "burglary report" -- even though nothing was reported stolen -- and in it, mentioned the connection to Shaw.

Cops later spoke with Shaw on the phone and the USC football player denied ever being at the building.

USC says it's investigating Shaw's claims that he saved his nephew from drowning Saturday night -- and injured his ankles jumping off a 2 story building to rush to his nephew's aid.

Cops tell us they're going to re-interview everyone involved in light of new information.