"No post is permanent in a democracy. If a person having appropriate authority calls me (asking to quit), then I will certainly think over it," Raj Bhavan sources quoted the 82-year-old Sankaranarayanan as saying.
They said Union Home Secretary Anil Goswami called Sankaranarayanan two days ago.
"The Union Home Secretary called the Governor two days ago with the message (to quit). The Governor spoke to some mediapersons and made his reaction known," sources told PTI.
Sankaranarayanan has been serving as Governor of Maharashtra since January 22, 2010.
He took oath as Governor of Maharashtra for a second time on May 7, 2012 after the President granted him a fresh term of 5 years.
The Narendra Modi government has started the process of removing some Raj Bhavan occupants appointed by the UPA government.
Uttar Pradesh Governor B L Joshi had yesterday resigned after being reportedly nudged to do so but some others, including Sankaranarayanan, are said to be holding out.