Ms Morgan is now asking Mr Hammond for "specific confirmation that all efforts are being made to encourage as diverse a range of candidates as possible" and that recruitment processes for the bank's policy committees follow rigorous standards used for other public appointments.
"The committee would be interested in taking evidence from you (or the most appropriate minister or senior official) on this shortly".
"An aim of the Commissioner for Public Appointments is to achieve greater diversity of public appointments".
She raised the concerns as the committee confirmed the appointments of the two newest recruits to the Bank's rate-setting monetary policy committee, Silvana Tenreyro and Sir David Ramsden.
"In the future, the committee expects to be provided, prior to appointment hearings, with diversity data on the candidates applying to the associated position".
The Bank of England had two female members on the MPC just earlier this year.
Morgan also demanded the Treasury, which appoints MPC members as well as those on the financial policy committee, "publish recent historical data about the applicants for MPC and the FPC membership (internal and external)".
Silvana Tenreyro is the only woman on the MPC after Kristin Forbes finished her term.
Ms Hogg had replaced outgoing MPC member Minouche Shafik this spring.
Earlier this year, BoE deputy governor Charlotte Hogg resigned after the committee issued a damning report over an undisclosed conflict of interest involving her brother.
The committee can not prevent an appointment by the Treasury to the Bank of England, but the government would be forced to act should it issue a negative verdict. It's two-thirds male, one-third female.
He said this may be a problem with a "culture of economics", that is not replicated in other professional field such as law, which attracts a far higher proportion of women. It is due to meet for its first evidence session next Tuesday.
The Bank's Governor, Mark Carney, said that there was no pay gap by the equal pay for equal work measure, but that the 21pc pay gap overall for the Bank reflected a serious lack of senior women in the organisation.
However, he admitted there was a gender pay gap at Threadneedle Street because "there's a lot more men than there are women" in senior roles.