Teenage striker Cofie, a season-long loan signing from Manchester United, is one of several new Blades players hoping to make their league debuts.
"We've got a few lads who will be assessed before the game on Saturday," manager Danny Wilson told the club's official website.
"They include Matt Hill, John Cofie, Ryan Flynn and Chris Porter. They've got slight niggles and at the moment we don't know how they will respond to treatment before the weekend."
Wilson has no other injury or suspension worries, while close-season arrivals Mark Howard, Darryl Westlake, Tony McMahon, Shaun Miller and Nick Blackman, who scored in the Capital One Cup defeat to Burton last weekend, could all make their first league appearances for the Blades.
Shrewsbury look set to have a full-strength squad available for their League One opener at Sheffield United after Darren Jones returned to training.
The defender missed last Saturday's 4-0 Capital One Cup defeat at Leeds with a calf problem but was back with his team-mates this week and has declared himself fit for the Bramall Lane clash.
Fellow defender Jermaine Grandison sat out of training at the start of this week having turned his ankle at Elland Road but he is also expected to be okay.
That means manager Graham Turner is likely to have a fully-fit squad to select from as Shrews look to start life in League One with a positive result against the Blades, who will be desperate to go one better than their agonising play-off final defeat in May.
Strikers Tom Bradshaw and Ryan Doble were both unused substitutes for Wales' Under-21 side in their 1-0 home defeat to Armenia on Wednesday night.