Ms Pushkar, wife of Congress parliamentarian Shashi Tharoor, was found dead in a south Delhi hotel room in January 2014.
The police told a bench of Justice GS Sistani and Justice Chander Shekhar that this mode of investigation would take a maximum of eight weeks after which they will file a report.
Forensic psychology is an emerging field which makes up an integral part of criminal investigation, prison and profiling systems, which is now used in some developed countries.
The bench asked the police why they want to start a new method of probe in late 2017 when investigation into the case began back in 2014. "Should any investigative agency drag the probe for so long?" the court said.
Additional Solicitor General Sanjay Jain, who appeared for the police, said this new tool of investigation will ensure "no stone is left unturned".
The bench told the police to file an affidavit within two weeks placing on record the approximate time that would take to finish the probe.
During the hearing, BJP leader Subramanian Swamy, who had sought a court-monitored probe into Ms Pushkar's death, said the Indian Premier League was also an angle which needed to be examined in the case. He sought to rope in the Enforcement Directorate in the case.
The court said it will consider his plea at an "appropriate stage". "We do not want to create any distraction at this moment," the court said and listed the matter to October 26.