Mark Carne, who will step down in the summer as chief executive of the company responsible for rail infrastructure, said people wanted rail services to reflect their lifestyles.
Five lines on the London Underground have run a 24-hour service since 2016, with services also running around the clock on the London Overground line between Highbury and Islington and New Cross Gate.
Mr Carne told the Times the public sector company was looking at its systems for inspecting and repairing the railway to prepare for round-the-clock services.
Stressing the importance of Network Rail staying ahead of demand, he told the paper: "If you have a 24-hour Tube, it is not going to be long before people want 24-hour availability of rail systems.
"I am anticipating that my customers - the train operating companies - will come to me in the not-too-distant future and tell me they want to run 24-hour trains.
"And I have got to be prepared for that and that's why we're thinking today about what that would look like."