The new hospital in Sutton is one of three options put forward by consultants commissioned by Epsom and St Helier University Hospitals Trust.
The others are to build a new hospital on either the St Helier site in Carshalton or the Epsom site.
The BBC said the hospital trust had commissioned consultants to “build a new super hospital for the area” on the former Sutton Hospital site – which is understood to be the “preferred option”.
One of the consultants on the train was heard to say they were “making progress” with Mr Elkeles on the plans, according to the BBC.
Plans to merge Epsom with Ashford and St Peter’s Hospitals in Surrey were halted in 2012.
Both Epsom and St Helier were part of the Better Services Better Value review of NHS services in the area, which was abandoned in February 2014 after previously recommending that the A&E and maternity departments at Epsom be closed.
In a statement Mr Elkeles said: “The Trust Board has always been very open that it is committed to retaining both hospitals for at least the next five years – and that remains the case.
“At the same time it is right that longer term planning should start now to tackle the serious problems facing local services and local NHS buildings, many of which were built in the 1930s and mean patients are being treated in inadequate conditions.
“However this is a long term plan and any of the options being looked at here are many years away from being implemented and will need a lot more discussion, agreement and consultation before they happen.”