Six persons including three "prime witnesses" in the case were already put through lie detector (polygraph) test and sources indicated that the police may go for carrying out the test on Tharoor.
When asked about it, Delhi Police Commissioner B S Bassi said, he was not aware of any such move, but said it was up to the investigating officer to do what he deemed fit.
As per the procedure, the prosecution will have to move a plea before the court seeking permission to carry out the test and it will depend on whether Tharoor gives his consent for it or not.
Last month, the Delhi Police had approached a city court for permission to carry out lie detector test on Narain Singh, who is domestic help of Sunanda's husband and Congress MP Shashi Tharoor, driver Bajrangi and family friend Sanjay Dewan.
The court had later allowed the investigators to conduct the polygraph test on the three suspects with their consent.
Three others -- S K Sharma, Vikas Ahlawat and Sunil Takru -- had also undergone the polygraph test.
Tharoor has been questioned thrice in this case. Sunanda was found dead in the hotel suite on January 17 last year, a day after she was involved in a spat with Pakistani journalist Mehr Tarar on Twitter over the latter's alleged affair with Tharoor.
Investigators said they are trying hard to make a breakthrough in the high-profile case and are awaiting the report from the US Federal Bureau of Investigation to know about the kind of poison found in Sunanda's body.
Her viscera samples were sent to the FBI lab in Washington in February after an AIIMS panel concluded that the poison cannot be detected in Indian labs.
Police had accused Singh, Bajrangi and Dewan of concealing "material facts" like a power cut in room no. 345 at Leela Hotel on January 17, 2014 around 7 PM where Pushkar was found dead around 8 pm.
In January, police had claimed that Sunanda, 51, was poisoned, and registered a murder case against unknown persons.