The Lucknow bench of the High Court asked the state's counsel to seek the government's instructions on the PIL within a week.
A division bench of Justices Uma Nath Singh and Virendra Kumar Dixit gave its order on the plea filed by journalist Sanjay Sharma.
In his petition, the appellant had said Kumar, along with former Chief Secretary Neera Yadav, was convicted by a special CBI court in connection with a land allotment scam in Noida.
The petitioner had sought the court's instruction for dismissal of Kumar on the ground that a convict cannot continue to hold a public office.
Kumar, who was given a three year jail term and was also imposed a fine of Rs one lakh by the special court on November 21 last year, has appealed against the judgement.
The petitioner had demanded that Kumar should be dismissed from service during pendency of the appeal.
The bench has fixed January 28 as the next date of hearing.