Sheridan told BBC Radio Cumbria: "I'd say (we need) three or four players and we'll be OK."
The Bluebirds continue to monitor trialists Kevin Austin, Ben Jackson, Ciaran Donnelly and Shaun Pearson.
Former Swansea and Chesterfield defender Austin, 37, impressed Sheridan in the 1-0 friendly win at Penrith.
It's not about age, if you're still fit you can still play
Barrow joint-manager Darren Sheridan
"He's comfortable on the ball and a strong lad," Sheridan added.
"People speak well of him. My brother (Chesterfield manager John Sheridan) said he'd take him all day long.
"He is 37 but I didn't come to Barrow until I was 38. It's not about age, if you're still fit you can still play."
London-born Austin has made nearly 400 first-team appearances in a career that began with Saffron Waldren Town in 1992.
Goalkeeper Pearson is the brother of Barrow defender Mike Pearson, while Jackson was released by Morecambe this summer.
Former Blackburn midfielder Donnelly has also had spells with Blackpool, Macclesfield Town and Fleetwood.
Sheridan said: "They're still on trial and we've got to make a decision on them."
Sheridan, who scored the winner in the Penrith game, confirmed that captain Paul Jones will seek advice on the injury that forced him to sit out the 1-0 victory.
"He's got a little niggle on his Achilles so he needs to see someone about it.
"He doesn't want to make it worse so he needs to make sure he isn't going to cause my damage by training on it."
Source: BBC Sport
Source: BBC Sport