Mr Hammond is reportedly looking to have Ms McVey sacked and replaced by his deputy Liz Truss due to their strained relationship.
Ms McVey has also faced criticism by some working in the Treasury.
One individual said: “The only thing she knows how to do well is a blow dry.”
However, some of Ms McVey’s allies have accused Mr Hammond of taking offence to her due to her willingness to stand up to him and demand more funding for the Department of Work and Pensions (DWP).
This came just ahead of a report which stated the Chancellor may be obliged to allocate more money within his October 29 budget to bail out the DWP because of its project to combine the nation’s various benefits into Universal Credit (UC).
The project has seen multiple delays and rising costs in a model which aims to merge six different benefits.
UC’s original creator Ian Duncan Smith has called for an extra £2billion to be added to the scheme so that they can replace the funding which was cut by the then-Chancellor George Osborne around two years ago.
However, the current Chancellor is allegedly up in arms over Ms McVey’s handling of UC.
One individual working for the Treasury was also highly critical of her.
They said: “She obviously never deals with serious matters of state as there is never a hair out of place. She’s a pain in the arse and costing us money.”
Some of Ms McVey’s allies claimed last night that Mr Hammond only wants Treasury Chief Secretary Ms Truss to replace the welfare chief because she would be “more pliant”.
One ally said: “Esther has been a bit too successful in Government for Hammond’s liking – that’s the problem.”
A spokesman for Mr Hammond denied any allegations that he was looking to have Ms McVey replaced with Ms Truss.
They insisted the Chancellor had good relations with the Work and Pensions Secretary.
They also added that Mr Hammond had recently hosted a benefit in London on behalf of Ms McVey’s Local Tatton Conservative Association.
Source : EXPRESS