Carroll, a 36-year-old former England international, has been without a club since playing for French team Bordeaux last season.
Before that, he had a year-long stint with Amiens in the 2023/24 season.
Chelmsford City's manager, Andy Harrop, was asked about the potential signing but chose not to comment.
However, Harrop did express his satisfaction with the team's current roster, highlighting the presence of young, hungry players with a lot of potential for growth and development.
Chelmsford City finished the previous season in 11th place out of 24 teams in the National League South.