Alleging sexual harassment, Nisha Priya Bhatia, 51, sought quashing of the government recommendation to the President to appoint Justice Dattu as the CJI.
A division bench of Chief Justice G Rohini and Justice RS Endlaw said it will hear the matter on Thursday.
Additional Solicitor General Sanjay Jain appearing for the central government opposed the plea, saying the petition is frivolous and should not be entertained.
Bhatia in the plea stated: "Quash recommendations reported to have been made by government - as council of ministers - to the President to appoint Justice H.L. Dattu as the Chief Justice of India."
She alleged that she was a law student in 2011 when Justice Dattu began hearing all her court cases in the Supreme Court, her work place.
"He (Dattu) has since then contributed to her acute and intense sexual harassment even though - under the Vishakha guidelines of the apex court itself - he was obliged to protect her against it, even from the third party," the plea said.
The plea said Justice Dattu dismissed all her cases and she had also filed complaints against him with police, the National Commission for Women and the Delhi Commission for Women.
Bhatia, a 1987 batch Class 1 executive cadre officer in the Research and Analysis Wing (RAW), got compulsory retirement from the service in 2009.