Known only as Lewis, the boy was riding the Yamaha bike with a three-year-old named Eddie on the back, in Woldgate, Bridlington, opposite the travellers' site he lives on.
The bike crashed with a silver Nissan Almera, sending the youngsters flying about 70ft. Lewis was not wearing a helmet.
Yesterday, Eddie's 50-year-old uncle, who would only give his name as Isaac, said the toddler was "doing fine" and that Lewis was, hopefully, being woken from his coma later that day.
He told the Mail: "He is improving brilliantly. They have taken his breathing tubes off him. He is still in a critical condition, but he is making improvements. We are all hoping he will make a full recovery.
"We still feel like there is a ton of bricks weighing down on us all and everyone is still very quiet on the site, but we are keeping positive for Lewis. It is going to take one step at a time."
The driver, who suffered whiplash injuries, called an ambulance for the boys.
Witnesses to the accident, which happened at 12.40pm on Saturday, should call PC Steve Naylor on 101, quoting log 271.
