Sources have told Media Week that Daily Mail & General Trust (DMGT) executives held discussions as the best way to capture NotW readers.
One serious proposal put forward was to launch a mass-market title, to complement its mid-market Mail on Sunday.
Names thought to be considered for the tabloid include The Sunday and The Sunday Lite.
One source close to the situation said: "They would be foolish not to consider launching the title."
Other options thought to be under consideration include heavy price promotion of the £1.50 Mail on Sunday as a means of capturing some NotW readers.
launching a major direct marketing campaign, hitting 1.5 million houses. But sources have told Media Week that executives have no immediate plans to launch the title in the market, until they had a sense of how the Sunday market would pan out in light of NotW's closure.
It is thought they are in the process of running dummy copies of the tabloid.
DMGT is likely to wait at least a month before launching such a title, which would compete against the Richard Desmond's Star on Sunday and Trinity Mirror's The People and Sunday Mirror.
The internet domain name thesunday.co.uk was registered on July 7 by a party called Colin Wilson Engineering.
DMGT currently publishes the Daily Mail, Mail on Sunday and the free morning newspaper, Metro.
The Mail on Sunday reported a circulation of around 1.9 million in May this year.
DMGT declined to comment.
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