Home Ministry sources said the 80-year-old Governor has tendered his resignation.
However, TV reports said that the West Bengal chief minister Mamata Banerjee is not awared of any such developments.
On Friday, June 27, he was questioned by the CBI as a witness in the infamous VVIP Chopper deal case in Kolkata.
CBI sources had said Narayanan, who was then the National Security Adviser (NSA) and Goa Governor BV Wanchoo as head of the elite Special Protection Group (SPG), were part of meetings where specifications for the helicopters were changed.
According to the CBI, both Wanchoo and Narayanan were part of meetings which led to the the high ceiling of the VVIP choppers sought being reduced, enabling Agusta Westland - an Italian chopper manufacturer - to enter the picture.
On June 17, West Bengal Chief Minister Mamata Banerjee had rushed to meet MK Narayanan, who was reported to have been pressurised to tender his resignation.
Narayanan is a former IPS officer who had served as director of Intelligence Bureau. Before being appointed as governor of West Bengal in January 2010, Narayanan was the National Security Advisor during the previous Manmohan Singh government.
The resignation came weeks after Union Home Secretary Anil Goswami had telephoned some of the Governors, appointed by the previous UPA regime, to step down after the Narendra Modi government assumed charge.
Nagaland Governor Ashwani Kumar, Uttar Pradesh Governor B L Joshi and Chhattisgarh Governor Shekhar Dutt have put in their papers in the last few days.
All the four governors who have resigned so far are either former IPS or IAS officers. Joshi and Kumar are former IPS officers while Dutt is a former IAS officer.
The NDA government is reportedly considering appointing some BJP veterans as Governors in around ten states.