Transport Secretary Chris Grayling is said to be preparing for an announcement to be made on Thursday.
The BBC has suggested the review could look at how issues such as those faced by the East Coast Mainline can be avoided in the future.
It will focus on the “balance of public and private sector involvement” in the future, the Sun newspaper reports, and how to restore faith in privatisation, designed to see off growing calls for the trains to be re-nationalised.
The Transport Secretary has hired John Lewis boss Keith Williams to lead a 12 month “root and branch” inquiry into the franchise system to “rebuild public trust” in the network, it adds.
A spokesman for the Department for Transport, when approached by The Yorkshire Post, said: “Privatisation has helped transform our railway – doubling passenger numbers and delivering more services, extra investment and new trains.
“We are absolutely committed to improving journeys and are always examining ways to improve how the railway serves passengers.”
It comes as rail services on two operators faced disruption today because of a fresh strike in the long-running dispute over guards on trains.
Members of the Rail, Maritime and Transport union (RMT) on South Western Railway (SWR) and Arriva Rail North (Northern) walked out for 24 hours.
Hundreds of services were cancelled and buses replaced trains on some routes.
The RMT said its members mounted picket lines outside stations and were solidly supporting the action.
Reports of a review into rail franchising are a "blatant and desperate effort to kick the continuing chaos on Britain's railways into the long grass," the union added.
General secretary Mick Cash said: "It won't work as it's clearly a desperate stunt by a Government clutching at straws which is ideologically opposed to the British people owning and running their railways.
"The only solution to the current rail franchise shambles is an end to private greed and a return to public ownership."
Paul Plummer, chief executive of the Rail Delivery Group which represents the rail industry said: “We have been saying that the time is right for root and branch reform of the railway so it can better leverage the innovation and investment required to deliver more for passengers, communities, businesses and taxpayers.
“Working together the public and private sectors in rail have achieved much over the last 20 years, but now is the time to renew that partnership to ensure Britain has the railway it needs for the next generation.”