Rovers announced the signing of Swansea forward Barrow on a deal through to November 10 subject to international clearance on Monday, and the Welsh club have given permission for him to feature in this season’s competition.
Boss Gary Bowyer is expected to make changes from Saturday’s 2-1 Sky Bet Championship loss to Wolves and the likes of Jason Steele, Matt Kilgallon and Bangaly Fode-Koita could also come into the first XI.
Midfielder Chris Taylor (groin) remains the only absentee from Bowyer’s squad.
Liam Lawrence and Liam McAlinden are pushing to start for Shrewsbury after their opening-day defeat to Millwall.
James Wesolowski and Nathaniel Knight-Percival are still unavailable as they continue to recover from long-term knee injuries but have returned to training.
Shrewsbury beat Blackpool, Leicester and Norwich last season before losing to eventual winners Chelsea in the fourth round.
Boss Micky Mellon told the club’s official site: “We’re aware of their threats and we’ll try to nullify them and take the challenge on. We’ve prepared the players, dusted them down and we believe they’re ready.”