Tied for second place with five nominations each, including best drama, are the Iran hostage-crisis thriller Argo and the slave-turned-bounty-hunter tale Django Unchained.
Jessica Alba announced the list of nominees alongside Megan Fox and Ed Helms in Hollywood.
Other best-drama nominees are the shipwreck story Life Of Pi and the Osama bin Laden manhunt thriller Zero Dark Thirty.
Day-Lewis, who lives in Wicklow, is up against Richard Gere as a deceitful Wall Streeter in Arbitrage; John Hawkes as a polio victim trying to lose his virginity in The Sessions; Joaquin Phoenix as a Navy veteran under the sway of a cult leader in The Master; and Denzel Washington as a boozy airline pilot in Flight.
Dramatic actress nominees are Jessica Chastain as a CIA analyst hunting Osama bin Laden in Zero Dark Thirty; Marion Cotillard as a whale biologist beset by tragedy in Rust And Bone; Helen Mirren as Alfred Hitchcock's strong-minded wife in Hitchcock; Naomi Watts as a woman caught up in a devastating tsunami in The Impossible; and Rachel Weisz as a woman ruined by an affair in The Deep Blue Sea
Period drama Downton Abbey looks set to repeat its success of last year after picking up a handful of nominations for the awards.
It is up for the best television drama series award along with US shows including Boardwalk Empire, Breaking Bad and Homeland.
Downton scooped the award for best television miniseries last time out. Another British hit, Sherlock, got a nod with a nomination for Benedict Cumberbatch as best actor in a TV mini-series.
On the comedy front, Zooey Deschanel was nominated as best actress in a TV comedy for New Girl, while Modern Family is up for best TV comedy.
The 70th annual Golden Globe Awards, voted for by members of the Hollywood Foreign Press Association, will be held on January 13.