According to reports, Mr. Hammond is seeking to have Miz Truss dismissed and replaced by Ms. McVey because of their tense relationship.
Ms. McVey has also faced criticism from some who work at the Treasury.
One individual said: "The only thing he knows how to do well is a sharp blow".
However, some of Mrs. McVey's allies have accused Mr. Hammond of being offended because of his willingness to face it and demand more funds for the Department of Work and Pensions (DWP).
This happened just before a report indicating that the Chancellor could be required to allocate more money within his budget on October 29 to rescue the DWP because of his project to combine the various benefits of the nation in Universal Credit (UC).
The project has experienced multiple delays and rising costs in a model that aims to merge six different benefits.
The original creator of the UC, Ian Duncan Smith, asked that an additional £ 2 billion be added to the plan so that they can replace the funding that was cut by the then Chancellor George Osborne about two years ago.
However, the current chancellor is supposed to be suspended for the management of UC by McVey.
An individual who worked for the Treasury was also very critical of her.
They said: "She obviously never deals with serious matters of state, since there's never a hair out of place, she's a pain in the ass and it's costing us money."
Some of Mrs. McVey's allies stated last night that Mr. Hammond only wants the Chief Treasury Secretary, Ms. Truss, to replace the Chief of Social Welfare because she would be "more flexible".
An ally said: "Esther has been too successful in the government's taste for Hammond, that's the problem."
A spokesperson for Mr. Hammond denied any allegation that he was seeking McVey to be replaced by Ms. Truss.
They insisted that the Chancellor had good relations with the Secretary of Labor and Pensions.
They also added that Mr. Hammond had recently received a benefit in London on behalf of the local Tatton Conservative Association of Mrs. McVey.