The owner of the Evening Standard and Independent is reported to have made a move to buy the Metro newspaper from the DMGT.
DMGT, publisher of the Daily Mail and Mirror, has been considering a sale of the Metro as part of a broader business review.
Metro saw a 9% decline in underlying revenues last year to £65m and suffered a 12% fall in operating profit.
The newspaper has been valued at between £25 and £35m.
According to The Telegraph, ESI Media boss Evgeny Lebedev is said to be interested in adding the Metro to its portfolio with a view to using its nationwide distribution network to launch regional versions of the Standard.
DMGT has not commented on the reports.