Phillip Harkins, 35, is accused of shooting dead 22-year-old Joshua Hayes in Jacksonville, Florida, in 1999 then fleeing to the UK.
The Greenock native laid low from authorities until he caused the death by dangerous driving of 62-year-old ran Jean O'Neill in the town in 2003.
Extradition proceedings started the week after the crash and he has spent more than 11 years waging a court battle to avoid being sent back to the US.
Mr Hayes' son, Josh Jr, who was seven at the time of the murder on August 10, 1999, said he wants Harkins to face justice.
Josh said: "I think that Harkins is pathetic. He doesn't care about anyone else. I think that he's a killer, a cold-blooded killer."
Since the extradition proceedings began in February 2003, three Home Secretaries have signed off paperwork to send Harkins back.
But he is still behind bars at London's Wandsworth prison.
Last month he was allowed to seek another judicial review, the outcome of which is expected at the end of the year.