A bench of Justices R K Agrawal and A M Sapre reserved its verdict after hearing the arguments of petitioner NGO Common Cause and Attorney General K K Vengugopal, who opposed the plea.
Advocate Prashant Bhushan, appearing for the NGO, said Asthana's appointment was illegal as his name had surfaced in a diary recovered during a raid conducted by the Income Tax department.
He said the diary showed the name of Asthana as having received an illegal gratification from a company and CBI has recently registered an FIR for money laundering against the accused firm and some public servants.
Attorney General opposed the plea and said the CBI has not named him in the FIR and Asthana has an outstanding career.
He said Asthana, who was earlier an additional director in CBI, was looking after eleven zones and supervising high- profile scams including that of AgustaWestland, Kingfisher, Moin Qureshi and Hassan Ali.
The bench, after hearing the arguments of both the sides, said it will pass the order.
Demanding quashing of Asthana's appointment, the petitioner has also sought a direction to the Centre to transfer him out of the agency during the pendency of investigation.
It has alleged that the decision to appoint Asthana was "illegal" and "arbitrary".
The petitioner has claimed that the government and the selection committee had overruled the opinion of the CBI Director while appointing Asthana "in violation of the law".
While seeking Asthana's ouster, the plea noted the special director was the second in command in the CBI after the director and supervised almost all important cases being handled by the agency.