The state-owned company, which is responsible for maintaining Britain's railway system, has drawn up proposals for meeting the UK Government's legally binding climate-change targets.
The Department for Transport had asked Network Rail to examine the possibility of removing all diesel-only trains from the railways of England and Wales by 2040.
The company produced a list of recommendations on how best to achieve that goal, and proposed that the 30-mile stretch of railway should be electrified.
The line serves stations at Bilbrook, Codsall, Albrighton, Cosford, Shifnal, Telford, Oakengates and Wellington.
The plans, which propose that almost all unelectrified parts of the West Midlands rail network should be converted, will now be submitted to the Government for consideration as part of its Comprehensive Spending Review.
The blueprint has been welcomed by regional transport body Midlands Connect, which said it could potentially represent the biggest rail revolution in more than a century.
The body, which includes 22 local authorities across the region, said the plans would not only improve the environment, but would make for a better service for passengers and create skilled jobs in the region.
Maria Machancoses of Midland Connect said: “This welcome announcement by Network Rail could unleash a rail revolution in the Midlands not seen in a hundred years.
“It will create skilled jobs, help level up the economy and help the UK to meet its net-zero target. But not only that, passengers will see improved reliability and faster journeys.
“The historic report recommends the electrification of almost all the Midlands rail network over the next few decades."
Mrs Machancoses said the next stage would be to work with Network Rail and the Department for Transport to help draw up a list of priorities and a proposed timetable.
"The Government’s agenda is – rightly – build back better and build back greener and we are supporting that every step of the way," she said.
Paul McMahon, of Network Rail, said electrifying lines which currently relied on diesel trains was a logical way of reducing carbon emissions, given that they derive their power from nuclear power stations.
But he did not provide a timescale for when work on the line should be carried out, saying it would form part of a 'long-term, stable and efficient programme of electrification which will last for at least 30 years, alongside the introduction of new technology'.
At the moment all direct trains between London and Shrewsbury have to use diesel power, even though most of the route is electrified.
Avanti West Coast, which took over the franchise to run inter-city services throughout the West Midlands, Staffordshire and Shropshire in December last year, has already announced it will be replacing the existing Super Voyager diesel trains with new bi-mode hybrid trains.
These are able to use diesel power between Shrewsbury and Wolverhampton, and then switch to electric power once they reach the electrified route between Wolverhampton and London.
The company hopes the new trains, which form part of a £350 million investment, will be in use by 2022, and that all diesel-only Super Voyager trains will have been phased out by the end of that year.