The incident in St Lawrence Street, Greenock, saw a man struck by a car at around 1:15am on Wednesday.
The vehicle sped away from the scene and the 22-year-old made his way to Inverclyde Hospital.
Officers are trying establish if the car - dark-coloured and with damaged windows - was driven deliberately at the man.
Detectives are also investigating reports of a disturbance around the time of the incident, which may be linked to it.
Detective Inspector David Wagstaff said: “Our inquiries are in the very early stages as we try to establish the exact circumstances of what has happened and why.
“I would ask local garages to get in touch with us if they receive or have received any damaged, dark- coloured cars for repair since 1.15am on Wednesday morning, in particular damaged windows or bodywork.
“If anyone has any information which could assist us then please do contact us.
“Do not think your information is not important or relevant as it could prove vital in our investigation.”
Officers are carrying out door-to-door inquiries and checking CCTV footage.
The man was released from hospital following examination.
Anyone with information is urged to call CID officers at Greenock Police Station via 101 quoting incident number 0211 of Wednesday, or anonymously contact Crimestoppers on 0800 555 111.