The plea has been filed in the backdrop of the May 7 top court judgement that had struck down an amendment in a state legislation allowing former chief ministers to retain government accommodation even after demitting office.
The father-son duo had earlier moved the UP government seeking two years' time to vacate their official residences and shifting to their private accommodations in Lucknow.
The former chief ministers, in their plea filed through advocate Garima Bajaj, have sought appropriate time to vacate their official bungalows.
The top court had on May 7 held that former chief ministers of Uttar Pradesh cannot retain government accommodation after demitting office and had said that a chief minister was at par with a common man once his or her term ends.
The top court had passed the order on a petition filed by an NGO Lok Prahari challenging the amendments made by the Akhilesh Yadav government to the 'UP Ministers (Salaries, Allowances and Miscellaneous Provisions) Act, 1981'.
The court, in its 29-page order, had said once such persons demit public office held by them, there is nothing to distinguish them from the common man.