The ex-England international is available after playing a season with fallen French giants Bordeaux. Before then, Carroll had a year with L2 Amiens for the 2023/24 season.
Carroll, now 36, is said to be in talks with Chelmsford about the new campaign.
Chelmsford boss Andy Harrop told the outstanding Non-League Paper: "No comment.
"I am really happy with what we've got in. We've got real quality, a lot of youth, a lot of players really hungry, which is great. They're all good ages as well.
"We believe there is a lot of development in all those players we've signed and that's the DNA we're going to go with. We've got some young players who have played a lot of games already."
City finished 11th out of 24 teams in the National League South last season.