The blue Peugeot bike was hit by a blue Jaguar X-type at the Carr Lane East and Dwerryhouse Lane junction in Norris Green, Liverpool, on Wednesday 13 January.
The 27-year-old motorcyclist was left with internal injuries and remains in a critical condition in hospital.
A 39-year-old man is in police custody.
An investigation is ongoing and a number of lines of enquiry are being pursued, police said.
Detectives are continuing to appeal for witnesses.
Det Ch Insp Mark Kameen said: "We believe that someone could have information that could help us with our investigation and we would urge anyone who hasn't already contacted us to get in touch. Any information they have could be vital."
Anyone with information is asked to contact police or Crimestoppers.
A man has been arrested on suspicion of attempted murder after a crash between a motorcycle and a car which left the rider in hospital.