Rovers will vie for a place in the semis with the Blades, the team three places ahead of them in the second tier, at Bramall Lane on Sunday.
Getting through would see them make a maiden trip to the new Wembley and reach the last four for the first time since 2006-07.
Tomasson, who saw his side win 2-1 at top-flight Leicester in round five having also triumphed on penalties at West Ham in the Carabao Cup earlier this season, said: “I would actually have rather played a Premier League side at home.
“First of all to give our fans the experience, and second, it’s also nice to try to win against a Premier League side – we’ve been able to do that twice this season, West Ham and Leicester.
“Against Nottingham Forest (a 4-1 home defeat in the Carabao Cup) I changed 11 players before the game, so it was a little bit more difficult to win that game. But I would rather have that.”
Blackburn’s FA Cup run this term has also featured victories at Norwich and Birmingham, the latter in a replay.
And Tomasson said: “It’s crazy, we’re playing every game away!
“We are doing well when we are playing away, but I would rather have played at home because I think our fans deserve a home game at this stage.
“On the other hand, I think we brought to Leicester, where we played extremely good against a Premier League side and won (which was) well deserved, around 3,000 supporters – it sounded like 25,000, 30,000.
“Now we are bringing almost 6,000 to Sheffield, (wouldn’t) it be great if those supporters could make a sound for 50,000, which would help the team a lot.”
Blackburn have won six of their last seven games in all competitions, including a 1-0 league victory over Paul Heckingbottom’s United on March 4 – a contest Tomasson says has “no impact” on Sunday.
Rovers will be without on-loan winger Sorba Thomas, who is cup-tied having played for parent club Huddersfield earlier in the competition.
While Thomas Kaminski is nearing a return from a knee injury, Tomasson has said the goalkeeper will not be starting on Sunday.