"The board of Trinity Mirror plc notes the recent media speculation and confirms that it is at an early stage of discussions towards taking a minority interest in a new company comprising certain of Northern & Shell's assets.
"No offer has been made and there is no certainty that any agreement will be reached," Trinity said in a statement.
It is the second time in under a year that Trinity has opened talks with Northern & Shell, which owns the Daily Express and Daily Star titles.
Mr Desmond acquired the titles in 2000 for £125 million.
A tie-up between the left-leaning Mirror and the Brexit-backing Express would raise eyebrows but could make commercial sense.
The print media industry is grappling with a decline in print advertising and any combination could herald cost savings and a shared cut of a larger advertising pool.
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