Two of the football great's daughters -- Gianinna, 31, and Jana, 24 -- have accused Luque of responsibility in Maradona's deteriorating health.
Maradona underwent surgery on November 3, just four days after he celebrated his 60th birthday at the club he coached, Gimnasia y Esgrima.
However, he appeared in poor health then and had trouble speaking.
Maradona had battled cocaine and alcohol addictions during his life.
He was suffering from liver, kidney and cardiovascular disorders when he died.
"The last time Gianinna visited Maradona she noticed he was very swollen. In the weeks before his death he displayed physical and cognitive deterioration," said Rodolfo Baque, a lawyer for one of the two nurses being investigated.
Maradona is an idol to millions of Argentines after he inspired the South American country to only its second World Cup triumph in 1986.
An attacking midfielder who spent two years with Spanish giants Barcelona, he is also loved in Naples where he helped Napoli win the only two Serie A titles in the club's history.