The Giants don't use their franchise tag very often and it appears they will likely not use it this year.
NFL Network's Ian Rapoport spoke with John Mara and tweeted that the team's co-owner said the Giants will "probably not" apply the franchise tag to any Giant.
The Giants are one of seven teams that have only used their franchise player designation three times or fewer on offense, defense or special teams since the system began in 1993, according to ESPN Stats and Information. They have used it on tackle Jumbo Elliott (1993), running back Brandon Jacobs (2009) and last year on punter Steve Weatherford. The Giants used the tag on Jacobs and Weatherford in an effort to later reach a long-term deal. (Here's a look at how the Giants' usage of the franchise tag compares to the rest of the NFL).
Tackle Will Beatty is considered to be the Giants' biggest free agent priority. If the Giants were to use the franchise tag on Beatty, perhaps in an effort to work out a long-term deal, the projected non-exclusive franchise player tag for an offensive lineman is $9.66 million.
Considering how the Giants likely need to clear more cap space to sign free agents, their own draft picks and tender restricted free agents like wide receiver Victor Cruz and safety Stevie Brown, it makes sense for Mara to say that the team will likely not opt to use its franchise tag.