The National Secular Society understands Harman will table an amendment to extend the bill, which aims to abolish hereditary peers in the House of Lords, to the 26 Church of England bishops who are given seats as of right.
Earlier this year, the NSS worked with a cross-party group of MPs to similarly amend the bill. Labour whipped MPs to vote against the amendment, which was defeated.
The bill has now reached the House of Lords where new amendments can be tabled. The bill will have its second reading in the Lords on Wednesday.
Harman's potential amendment comes as new polling suggests only one in five Brits support the bishops' bench. Calls for the resignation of bishops criticised in the Makin review into child sex abuse allegations in the Church of England and other scandals are also growing.
Survivor: Archbishop of York's actions "very, very underhand"
Stephen Cottrell, the archbishop of York, will temporarily take over Justin Welby's duties as archbishop of Canterbury in January. Welby resigned after the Makin review revealed he failed to adequately respond when informed of John Symth's abuse in 2013.
But a survivor of abuse has now called for Cottrell's resignation following his role in a separate abuse scandal.
In the 1980s, Matthew Ineson, then a teenager, was raped by Church of England priest Trevor Devamanikkam. In 2013, Ineson disclosed the abuse to then archbishop of York John Sentamu and other senior CofE clergy.
Ineson received a one-line letter in response from Sentamu: "Thank you for copying me into the letter which I have read, please be assured of my prayers and best wishes during this testing time." Ineson said Sentamu did "absolutely nothing".
Last year, an independent review commissioned by the CofE confirmed Ineson had been sexually abused by Devamanikkam. It found Sentamu and other bishops had failed to act on Ineson's disclosures.
In 2023, Sentamu, then in the Newcastle diocese, was suspended by the bishop of Newcastle for rejecting the findings of the review and refusing to apologise for his inaction.
"Safeguarding is very important but it does not trump church law", he said. Sentamu sits by rights in the Lords.
In October, Welby and Cottrell wrote to the bishop of Newcastle, Helen-Ann Hartley, seeking Sentamu's reinstatement. Ineson said he felt "used" by Cottrell, who had 'gone behind his back', and described his actions as "very, very underhand".
Hartley described the letter as "coercive". Separately, she accused bishops who failed to condemn the Church's coverup of abuse of "careerism".
General Synod member and Anglican priest Robert Thompson, who spoke at this year's NSS conference, has called for all bishops named in the Makin review to surrender their seats in the Lords pending further investigation. These include Justin Welby; former archbishop of Canterbury George Carey; and the bishop of Lincoln, Stephen Conway.
Nicky Morgan: Time to debate bishops' bench "very firmly has come"
Former culture and education secretary baroness Nicky Morgan said it would be "quite difficult" for those criticised in the Makin review to continue in their position, and the time to debate the bishops' bench "very firmly has come".
Morgan, herself an Anglican, said she was "horrified" by Ineson's story. Anyone who had "betrayed the trust" of a survivor should reflect on their position, she said.
Former conservative MP and culture secretary Nadine Dorries, who was sexually abused by an Anglican vicar as a child, has also called for the abolition of the bishops' bench.
She said she was treated like a "contagion" by bishops when she informed them of her abuse. Dorries described them as "completely out of their depth" and as having "no idea" how to handle complaints of abuse.
Alleging bishops were attempting to "cover up" abuse, she called the attempt to reinstate Sentamu "just shocking". Bishops have "let people down badly", she said, and resignation is their "only option".
NSS: 'Church's waning morality authority now in tatters'
National Secular Society spokesperson Alejandro Sanchez said: "We welcome the growing momentum to abolish the bishops' bench.
"Whatever remained of the Church's waning moral authority is now in tatters. Any argument that Anglican bishops bring a unique ethical insight to our legislature is entirely untenable.
"Guaranteed representation for one denomination of one faith has no place in a modern, pluralistic democracy like ours. If clerics wish to participate in our political life, they are welcome to do so – on the basis of equality, not privilege."