Carroll's future has been the subject of continued speculation this summer, with the England international linked with a loan move to West Ham United and Newcastle United.
Shelvey believes that Carroll has what it takes to turn things round and impress new manager Brendan Rodgers.
The 20-year-old told Goal.com: "Obviously, I've only played with Andy a few times last season but I know what he's about.
"It's not down to me whether or not he stays, it's down to the boss but Andy is a great player. I think he can fit in."
Liverpool play their first competitive game under Rodgers against West Bromwich Albion on Saturday, August 18.