Westminster-watchers believe Dr Fox, 52, who trained as a GP in Glasgow, has done his penance on the backbenches after resigning two years ago following the controversy, which involved his close friend Adam Werritty, a lobbyist who was allowed access to the Ministry of Defence.
Dr Fox, a Eurosceptic rightwinger, has been publicly supportive of the Prime Minister, particularly over the pledge to hold an in-out referendum, and is thought to be close to Tory election strategist Lynton Crosby. Other figures tipped for promotion include Sajid Javid, the Economic Secretary at the Treasury, Michael Fallon, the Business Minister, and Nadhim Zahawi, the MP for Stratford upon Avon.
Mr Cameron is also expected to promote a number of women MPs, including Esther McVey, the Pensions Minister, Helen Grant, the Health Minister, and Liz Truss, the Education Minister.
It is thought that most changes are likely to affect junior ministerial roles.
Speculation is also mounting that Ed Miliband, the Labour leader, could reshuffle some of his top team shortly. Among the changes here could be Rachel Reeves, No 2 to Ed Balls in the Treasury team, who could replace Liam Byrne in the Work and Pensions portfolio.