United, who return to Championship action on Saturday at home to Bristol City, are second in the table – a point ahead of third-placed Leeds – with just eight games of the regular season remaining.
After City, Chris Wilder’s Blades face Millwall, Ipswich and Nottingham Forest at Bramall Lane, sandwiched between away trips to Preston, Birmingham, Hull City and Stoke.
And Norwood, who was named in the Championship team of the year earlier this week, said: “I personally love playing at Bramall Lane, and I know the rest of the lads do as well.
“I remember around Christmas, when we played Derby and Blackburn at home, the atmosphere was fantastic and I think that's when the fans really started to believe that we could do something special this season.
“They got behind us and were really vocal.
“From our point of view, all we can do is ask them to stay with us and keep driving us forward if there’s a difficult period we come up against.
“As I say, there’s been times this season when they’ve made a massive difference and really driven us forward.
“And they can do that over the last four home games we’ve got left.”