The trio are being questioned about an incident which happened in Harbour Road, Lydney at 3pm on Sunday
A 33-year-old local man was taken to Gloucestershire Royal Hospital with minor leg and head injuries and later discharged.
Police believe a black Toyota Celica with the registration number H731 BGX was involved.
They are linking it to an assault in Station Road earlier where a 19-year-old woman from Coleford suffered a laceration to her hand which required hospital treatment.
A 30-year-old man from Cheltenham was arrested on suspicion of causing grievous bodily harm.
Following inquiries at the scene of the Harbour Road incident, police arrested a 23-year-old man and 19 year-old woman from Coleford and a 22-year-old man from Gwent on suspicion of attempted murder.
They are currently being questioned at Gloucester Police Station.
Officers are appealing for anyone who saw the Toyota Celica being driven in the area, before or after the collision, to get in touch.
Anyone with information should call the new non-emergency number 101, quoting incident 271 of September 25.
Alternatively, you can also give information anonymously on 0800 555 111.