The Post report termed the deal done "in principle," with an announcement not expected prior to next week. A Cubs official contacted by MLB.com would not confirm the report.
Marquis, who is due to earn $9,875,000 in 2009, had been perceived as one of the obstacles to the Cubs' earlier interest in acquiring San Diego right-hander Jake Peavy -- a proposed deal subsequently termed "dead" by both parties.
The Cubs will net a payroll savings of about $5 million in the exchange, according to the Post, assuming only about $1 million of Marquis' contract, while inheriting the $4 million still owed Vizcaino.
Vizcaino's 2009 salary calls for $3.5 million, with a 2010 option at $4 million, and a $500,000 buyout. The 34-year-old reliever appeared in 43 games for the Rockies last season.
Marquis, 30, has been a consistent winner despite escalating ERAs -- 4.53 last season while he went 11-9 in 28 starts. In the last five seasons, the first three with the Cardinals, he has won 65 games, posting a sub-4.13 ERA only once.
Tom Singer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.