Presley Gerber appeared under the influence of a substance when he checked into the luxury rehab home where he would later die ... TMZ has learned.

Sources who had contact with Presley in his final hours tell TMZ he did not appear sober when he arrived at the Santa Monica facility Saturday night, while seeking help for substance abuse issues.

As we first reported ... the 27-year-old model was found unresponsive at the home Sunday morning and cops responded to a suspected overdose call around 9:35 AM.

A spokesperson for the Santa Monica Police Department told us officers located an unresponsive individual at the facility and performed life-saving measures. Presley was pronounced dead approximately 10 minutes later.

His death is being investigated as a suspected drug overdose. No foul play is suspected, and an official cause of death has yet to be released.

Presley's family -- supermodel Cindy Crawford, businessman Rande Gerber and actress and model Kaia Gerber -- has asked for privacy as they grieve.