Diego Maradona died in November 2020, aged 60.
The family has questioned the circumstances surrounding the Argentine icon's death, and seven members of his medical team - including Maradona's doctor, psychiatrist and nurses - have been accused of inadequate care.
They deny the accusations.
In Wednesday's closing argument, the prosecutor representing Maradona's two daughters accused the staff of "murder" and called for prison sentences of up to 15 years for six of the defendants.
He said they had shown "brutal indifference" to the fate of the football legend.
Closing arguments in the trial in San Isidro, outside Buenos Aires, are expected to last about two weeks. A verdict is expected later.