Neither club has commented on whether such a trade discussion has taken place.
Earlier in the week, it was widely reported Marquis would have to be moved if a Peavy trade were to happen. Negotiations between the Cubs and Padres on a potential Peavy deal came to an end Thursday.
A Staten Island native, Marquis went 11-9 with a 4.53 ERA in 28 starts and one relief appearance in 2008.
The Mets bolstered their bullpen by signing Francisco Rodriguez and acquiring J.J. Putz from the Mariners, but they still need a starting pitcher -- likely a fourth starter, not an ace.
John Schlegel is an executive editor for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.