The move follows a similar invitation to tender mooted by Transport for London (TfL) in March, which cleared the way for an evening paper to rival Associated Newspapers Metro.
Last year, Daily Mail & General Trust offered to waive its rights to exclusive distribution of free papers at London Underground stations to close a regulatory investigation by the Office of Fair Trading (OFT). In March, the OFT accepted the arrangement.
Since then, there has been media speculation that News International was getting ready to launch a free evening paper, regardless of whether it won the contract with TfL. Without the contract, it could distribute the paper by hand or employ dump bins on pavements.
Other publishers believed to be interested in the TfL contract include Guardian Media Group and Trinity Mirror.
Network Rail said the winning bidder could either be two different newspapers or one newspaper delivered at both London Underground and railway stations. It would be distributed between 3pm and 9pm using the boxes installed for Metro.
The tender process is due to be complete by the end of June.
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