May is expected to name her top team in the coming days, and Hammond has been widely named as the likely inheritor of one of the government's most senior roles.
According to ITV political editor Robert Peston, Hammond will be made chancellor, while energy secretary Amber Rudd is to be named home secretary.
It means that two of the UK's most senior posts will be held by prominent Remain campaigners, both of whom backed May in the leadership campaign.
Other names linked the role of chancellor include business secretary Sajid Javid and leader of the house of commons Chris Grayling.
A Downing Street spokesman declined to comment.
An appointment to the Treasury would cap a steady rise for Hammond, who has led the foreign office for two years, but held frontbench and shadow frontbench roles consistently since his election in 1997.