According to Gary Myers of The New York Daily News, McDaniels and Patricia are "1 and 1A" in the eyes of new Giants general manager Dave Gettleman.
Giants owner John Mara said the team wants to hire an experienced coach, and Schwartz would qualify.
Schwartz is expected to interview in NY next week, while the Eagles are on a bye week entering the playoffs.
After firing Ben McAdoo a month ago, the New York Giants continued to clean house by removing general manager Jerry Reese from his longtime post. The inexperienced McAdoo was sacked just 12 games into his second season. "It's not impossible for you to succeed without that, but I think the more experience that that individual has as either a head coach or as a coordinator on either side of the ball, I think is very important". Four of his five seasons, though, ended with losing records.
Schwartz, who took over at the helm of the Detroit Lions before the 2009-10 season after the team's infamous 0-16 campaign, got the Lions to the playoffs as soon as the 2011-12 season.
Schwartz was unavailable for comment before the Eagles were to face the Cowboys in Sunday's season finale. Schwartz is one of the top defensive playcallers in the league. The Halethorpe, Maryland, native has held that title with the Titans (2001-08), Bills (2014) and Eagles (2016-present).
Schwartz is expected to interview with the Giants in the next week, while the Eagles - with an NFC-best record of 13-2 - are on the bye heading into the postseason. Steve Spagnuolo has since served as interim head coach.
McDaniels, who returned to New England following stints in Denver and St. Louis, has been the Patriots' offensive coordinator since 2012.