The award of the franchise to FirstGroup was scrapped on Wednesday because of bidding process "flaws".
The Times has reported that she learned of a potential flaw a week before the Cabinet reshuffle on 4 September.
The DfT says this was not the error that caused the process to collapse.
Three civil servants - who face possible further disciplinary action pending an investigation - have been suspended after the government admitted major failings over the contract to run the rail line.
BBC transport correspondent Richard Westcott said the department told him Ms Greening had been made aware of an area of "potential concern" but that she had been told it would "not affect the outcome".
She asked officials to check it further and it turned out to be a "minor error". The department insists it is not related to the main flaw that they found later on and which brought the whole process down.
Transport Secretary Patrick McLoughlin said a "terrible mistake" in evaluating the relative merits of four bids had been made by Department for Transport staff and that the fault lay "wholly and squarely" with the department.
Staff reportedly failed to include predicted passenger numbers and inflation forecasts in some of the risk assessments of the rival bids from firms.
They included Sir Richard Branson's Virgin Trains, which currently runs the route - which links London with Glasgow and Edinburgh via the Midlands and north-west of England.
Mr McLoughlin said the estimated cost of reimbursing the four companies for the cost of their bids would be Â£40m.
Meanwhile, the Public and Commercial Services union, which represents one of the suspended men, said it would ensure the inquiry examined all the issues, including ministerial involvement and oversight of the bidding process.
General secretary Mark Serwotka said: "The way ministers have sought to blame civil servants in the Department for Transport before any of the facts have been established has been deplorable but sadly not out of character.
"It is entirely consistent with the way the civil service is being treated by many ministers as an irritation, rather than as a professional body that works to ensure the smooth running of government."
Scotland's transport secretary has hit out at the handling of the franchise, saying the Scottish Government had been given no notice of the decision to scrap the FirstGroup deal.
In a statement at the Scottish Parliament, Keith Brown said: "The department's handling of the procurement process has been incompetent and shambolic. Most importantly, it has caused a great deal of confusion and speculation about arrangements for West Coast services after the franchise handover date of 9 December."
He said the Scottish government would be keeping a close eye on assurances which had been given by the Department of Transport that services would not be affected.
Former Transport Secretary Justine Greening did not know about the problem which led to the collapse of the West Coast Main Line franchise award, the Department for Transport has said.