Fife reporter, BBC Scotland news website
The line closed in 1969 as part of cuts imposed by Dr Beeching
A Fife MSP has said it would cost £20m to put trains back on the railway line between Leven and Thornton.
Tracks and signals are still in place from when the line carried freight to Methil docks, although they have not been sufficiently maintained.
Tricia Marwick said there was now major support for reopening the line and providing a service to Edinburgh.
Some campaigners also want to see the branch line to St Andrews reinstated to ease traffic congestion.
The SNP member for Fife Central has been leading a campaign to reopen the Leven line and said she was hoping to convince the transport minister of its merits.
She told the BBC Scotland news website: "It would be very simple to reopen it because it's never been closed.
"This line is still intact. It is still, in terms of Network Rail, a working railway for freight."
She did admit that work would be needed to upgrade substantial parts of the infrastructure, which has decayed in recent years through lack of use.
The reopening of the line is seen as having major benefits to the economy of Leven.
David Chalmers, of FSB Fife, said: "Providing that there is easy access in and out of the region then it is going to encourage businesses large and small to think about relocating along to Leven.
"That has to have benefits to the local economy and the local small businesses."
The line, which closed under the Dr Beeching era of the 1960s, was part of the branch line around the East Neuk of Fife.
A separate campaign is also under way to reopen the stretch from Leuchars to St Andrews.
Archive footage of St Andrews and Leven stations before closure
The town has no railway and tourist traffic, particularly around bank holidays, often causes congestion on the roads.
Jane Ann Liston, who is leading the campaign, said of the Easter holiday: "At lunchtime there were queues going all the way up the A91.
"It looked as if everybody had decided to come to St Andrews for Easter Monday lunch and, judging by the queues, they'd be lucky if they got afternoon tea."
The Liberal Democrat MP for North-East Fife, Sir Menzies Campbell, is backing the campaigns and has written to the transport minister supporting the reopening of the Leven line.
He said: "The case for Levenmouth is extremely strong and adds weight to the restoration of the St Andrews link.
"If Levenmouth is being viewed as a serious option then St Andrews should be treated as a similar priority."