The request was made by a delegation of 15 opposition lawmakers led by Congress party chief Rahul Gandhi. The lawmakers also demanded investigation into deaths of two associates of Loya.
Gandhi said the delegation of lawmakers received a "positive" response from the president.
In 2015 lawyer Shrikant Khandalkar died after falling from the sixth floor of a district court building. In 2016, district judge Prakash Thombre died after falling from the top berth inside a train coach.
"A special investigation team should be formed to investigate the cases," Kapil Sibal, a Congress party lawmaker said. "We don't believe in the central bureau of investigation (CBI) or the national investigation agency (NIA)."
Currently two petitions seeking an investigation into Justice Loya's death are being heard by the India's Supreme Court.
Justice Loya's case has become an important rallying point for the opposition against the Bhartiya Janta Party (BJP)-led government headed by Narendra Modi. At least 114 parliamentarians have signed the memorandum presented to the president.
Last month the apex court described the case as a "serious matter". Loya died of a cardiac arrest while he was attending a wedding in Nagpur city on Dec. 1, 2014.
Doubts about his natural death came under spotlight in November last year after media reports quoting Loya's family members raised suspicion over his sudden demise.
A report published in a local news magazine "Caravan" quoted Loya's family members saying he confided to them that the then Chief Justice of the Bombay high court, Justice Mohit Shah, offered a bribe of 15.5 million U. S. dollars (100 crore INR) to him for a verdict favouring Amit Shah.
After Justice Loya died, the judge who replaced him in hearing exonerated Amit Shah, ruling out his trial.
The CBI had alleged that Amit Shah, then local home minister of Gujarat, ordered the extra-judicial killings of his wife and a friend in 2005.
The case was moved from Gujarat state to the Bombay high court on the orders of Supreme Court after the CBI alleged that Amit Shah could influence the proceedings in his home state.