Weir was installed as the Blades' seventh permanent manager in as many years when he left his post as reserve team coach at Everton earlier in June.
The 43-year-old Scot had been tipped for a bigger role at Goodison Park under new Toffees manager Roberto Martinez, but instead he opted to make the move into his first senior management job.
Money is likely be tight at Bramall Lane, but Weir is convinced that some good deals could be carved out with players keen to make a name for themselves in English football for the first time.
"It's a market I know well. I know money's tight and it's an area I'll be looking at - not the only one, but there's definitely talent there," said Weir, who ended his playing days with Rangers in 2012.
"There are young players playing first-team football and players who can go on and get better. They're the types you want to get in who can improve themselves and improve your team.
"But I'm not going to go and get five or six - I've already got four in Jamie Murphy, Neill Collins, Ryan Flynn and Kevin MacDonald! Scots players travel well but I don't want to have eleven players from Scotland in my team.
"It's difficult because if they're the ones you know and that you trust then I can see why. But I've been fortunate having been in England for the last couple of years and my recent experiences have been in England so hopefully I have a grasp of players there as well."