The Giants reportedly have some interest in possibly bringing him back as a center next season, but it appears as though they will have some competition for his services.
Boothe, 30, appeared in all 16 games for the Giants, which included six starts at center.
Pro Football Focus has him rated as the No. 46 guard in the league in 2013, which is due in large part to his underwhelming rating as a pass-blocker.
Carrington, 26, should have a decent enough market based on his age, position and ability to play multiple positions on the defensive line.
Last year, Carrington was limited to playing in just three games after he suffered a torn quad and was subsequently placed on season-ending injured reserve.
We have Carrington listed as the No. 43 best available player in our Top 50 Free Agents list.