The government has refused to rule out a change in the law to allow employers to discriminate in favour of black or female job applicants.
Harman is said to want a clause in the forthcoming Single Equality Bill enabling employers to select ethnic minority applicants who are as qualified as white candidates.
A spokeswoman for the Government Equalities Office said: “Nothing has been decided yet. This idea is one of the things that has been looked at but no decision has been made.
“A government response to the Single Equality Bill consultation will be made sometime in the spring or summer, and this will indicate the direction of thinking.”
The spokeswoman said that under the proposal, where two candidates were equally suitable for the job, “it could be possible to give preference to a candidate from an under-represented group in some circumstances”.
It was revealed last month that a report commissioned by Harman had recommended all-black shortlists to increase the number of ethnic minority MPs. However, the Cabinet Office insisted such schemes would not be allowed for UK businesses.
Employers’ group the CBI said it was waiting for a full announcement on the contents of the Single Equality Bill before responding.