Trinity has not commented on the rumours and GMG has not named Trinity as a potential bidder, nor anyone else. However, it has admitted to being in a "very early stage" of a review process.
That has not stopped newspapers, such as The Telegraph, speculating that the two may be set to complete a deal for the Manchester title, which is printed at Trinity's Oldham site.
A spokesman for GMG said: "In line with its remit, GMG keeps its portfolio under review on an ongoing basis.
"Since the publication of the Digital Britain report, we have been considering the potential for further consolidation within the regional press sector, and as part of this there have been some exploratory talks regarding our regional media business."
Regional newspapers have been lobbying government for the right to exchange content and merge local titles.
If GMG were to sell the Manchester Evening News, it would end its association with the city of its birth. The Manchester Guardian was created in 1821 and became The Guardian when it moved to London in 1959.