The loss-making titles, which are part of the Independent News & Media group, could be sold off for £1, with DMGT taking on the loss-making papers' liabilities.
It is not clear whether discussions between the two companies have taken place. but one senior executive at DMGT said the likelihood of a bid is "highly possible".
A bid for the titles would come as IN&M chief executive Sir Tony O'Reilly faces pressure from rebel shareholder Denis O'Brien, who has built his stake in the company to 26%, to offload the two titles.
O'Reilly has to date resisted these calls, but the company must renegotiate a number of loans next spring and it is understood that the banks are unwilling to underwrite the company when its national newspapers are loss making.
DMGT declined to comment, while IN&M denied it was in talks with DMGT.
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