Sources told the NFL Network that the Giants view Collins as a great player, but believe the tag price for safeties ($11.15 million) is too high.
If the Giants don't use the tag on Collins before Tuesday's 4 p.m. EST deadline, he will enter free agency as one of the top safeties available, along with Earl Thomas, Tyrann Mathieu and Lamarcus Joyner.
Collins is a three-time Pro Bowl selection and was an All-Pro choice in 2016. He is the only player in the NFL to record at least 400 tackles and 30 passes defensed since the 2015 season. He is also the only safety in the league to register at least 95 tackles in the last four campaigns.
Sources told the NFL Network that the Giants previously wanted to put the tag on Collins, but the safety was unlikely to sign the tender and could have sat out the team's offseason programs.
The Giants selected Collins in the second round of the 2015 NFL Draft out of Alabama. He had 96 total tackles, one forced fumble and four passes defensed in 12 games last season.
In his four-year NFL career, he has 437 stops, eight interceptions, 4.0 sacks, three forced fumbles, 32 passes defensed and one defensive touchdown.