Public prosecutor JV Kendralkar informed Sessions Court Judge DW Deshpande that the prosecution was awaiting the state government's response in the matter and accordingly sought time.
Salman Khan's lawyer Shrikant Shivade opposed the prosecution plea and urged for fresh trial to commence immediately.
He also pleaded to the court to grant a short date to the prosecution for adjourning the case.
Judge Deshpande posted the matter for January 21 and directed the prosecution to get instructions from the government on the issue of appeal before the High Court.
The sessions court had earlier on December 5 ordered commencement of a fresh trial in the case.
The grounds for fresh trial was that Salman was not given opportunity to examine witnesses in the context of the enhanced charges of culpable homicide under Indian Penal Code Section 304(2) slapped on him during the trial.
Earlier, the actor was tried by a magistrate court for the lesser offence of causing death by negligence which attracts jail of up to two years.
After examining 17 witnesses, the magistrate court held that the higher charge of culpable homicide was made out against Salman and referred it to the sessions court.
The high-profile case dates back to September 28, 2002 when a SUV Toyota Land Cruiser allegedly driven by Salman Khan ran over some pavement dwellers in Bandra west, killing one and injuring four.