United will be confident of extending a 13-game unbeaten league run in the league that has taken them to the top of the table against the Blades, who have won only once in the top flight this season.
However, Solskjaer's men could find themselves knocked down to second by the time they kick-off as Manchester City can go top if they beat second-bottom West Brom on Tuesday.
United's fine form continued by knocking Liverpool out of the FA Cup on Sunday, winning a thrilling tie 3-2.
But Solskjaer is wary of his side slipping back into bad habits as they have done previously after good runs in his tenure.
"Now I want to see the reaction, how we can now mentally go again, against Sheffield United. That's the challenge now," said Solskjaer.