The 78-year-old retired Indian Police Service (IPS) officer was the Uttar Pradesh governor since 2009 and had enjoyed a good relationship with two successive chief ministers, Mayawati and Akhilesh Yadav.
An official who worked with him said that with the ascendancy of the Bharatiya Janata Party (BJP), Joshi was feeling uneasy as the Congress-led government had appointed him.
Joshi served as the Lt Governor of Delhi between 2004 and 2007 and was also the governor of Meghalaya and Uttarakhand before being shifted to Uttar Pradesh.
West Bengal governor MK Narayanan's resignation is also imminent within next 24 hours, some reports suggest.
Meanwhile, two Congress appointed governors- HR Bhardwaj of Karnataka and and JB Patnaik of Assam are holding a meeting with the President Pranab Mukherjee.
Unconfirmed reports said that Bhardwaj and Patnaik have also stepped down as the governors of Karnataka and Assam, respectively.
Patnaik told media persons that his meeting with the President was just a 'courtesy call' and asked, "why should I quit".
Rajasthan Governor Margaret Alva, who met PM Narendra Modi at his residence, will meet President at 6 pm today.
Kerala Governor Sheila Dikshit, Punjab Governor Shivraj Patil, Madhya Pradesh Governor Ram Naresh Yadav, West Bengal - MK Narayanan, Kamla Beniwal Governor Gujarat, K Sankaranarayanan in Maharashtra and Devendra Konwar in Tripura are also in the list of governors who might be replaced.
Reports also say that former Delhi chief minister Sheila Dikshit may be moved to a smaller northeastern state.
BJP veteran leaders like Dr Murli Manohar Joshi, Lalji Tandon and many others, who could not find a place in Prime Minister Narendra Modi's council of ministers, are most likely to be appointed as the new governors.
Joshi, who won from Kanpur, may be the next governor of Maharashtra.
Earlier, a report also said that former BJP senior leader Jaswant Singh is likely to be back in the party and he may be offered the post of Governor of Tamil Nadu.