Mr Cook, who was treasurer of Conservatives IN, is chairman of Sheffield-based engineering company William Cook Holdings.
According to a national newspaper, he is one of 48 politicians, donors and aides in line for knighthoods, and other titles, as part of Mr Cameron’s resignation honours list.
There are claims that the individuals concerned are being rewarded for failure because of Britain’s decision to leave the European Union. Mr Cook wrote an article for The Yorkshire Post on June 15 in which he challenged the then PM’s critics “to ask themselves whether they really want to risk their jobs and consider who they would prefer to be Prime Minister of this country”.
Reports suggest that four serving Cabinet ministers – Philip Hammond, Michael Fallon, David Lidington and Patrick McLoughlin – are set receive knighthoods.
Other titles could see George Osborne, the former Chancellor and Mr Cameron’s right-hand man, made a companion of honour.
This distinguished award is normally reserved for individuals over the age 65 who have provided nationally important service – Mr Osborne, who was sacked when Theresa May became PM last month, is just 45.
If sanctioned by the Cabinet Office, Mr Cameron’s resignation honours are likely to be the most contentious since Harold Wilson’s so-called Lavender List in 1976 – and the influence exerted at the time by the Huddersfield-born premier’s political secretary Marcia Williams.
Though Margaret Thatcher and John Major exercised their right to reward close colleagues and confidantes on their respective departures from 10 Downing Street, both Tony Blair or Gordon Brown declined to publish lists in order to avoid allegations of cronyism.