Officers believe the man may have been lying in the road at the time he was involved in a collision with a silver Mini car.
It happened outside Haven Cottage in Windsor Lane at around 6.15pm on December 31.
The man was taken to the Royal Shrewsbury Hospital with serious head and chest injuries but later transferred to the Queen Elizabeth Hospital in Birmingham where his condition is stable.
Police Constable Mark Booth, the investigating officer, said: “The scene of the incident is an unlit, narrow lane.
“I am anxious to hear from anyone who may have seen a man walking or lying in the road just before or after 6pm on New Year’s Eve. Anyone who thinks they saw him, or indeed witnessed the actual collision, should contact Shrewsbury police station on 101.
“We are continuing to investigate the circumstances and would welcome any information which might help.”
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