The Whites lost 1-0 to Championship leaders Burnley on Saturday.
Leeds defender Liam Cooper has insisted that a repeat of their performance against Burnley on Saturday will give the Whites a very good chance of getting a positive result against Birmingham, the Yorkshire Evening Post reports.
Steve Evans' men fell to a 1-0 defeat at Turf Moor but received plaudits for a promising effort against a side that look to be well on course to sealing automatic-promotion to the top flight.
And ahead of their game against the Blues, Cooper suggested that another performance of that calibre could go a long way to ending their four-match winless run on Tuesday.
"If we play like we did at Burnley then we'll give Birmingham a right good go," he told the Yorkshire Evening Post.
"They're another strong team, a hard place to go, but we're looking forward to it.
"Once we settled down [at Turf Moor] we looked the better team, we passed the ball well and we've given a Burnley team who'll probably be playing in the Premier League next year a good run for their money."
Gary Rowett's men have spent the majority of the year just outside the top six. And while they have fallen away in recent weeks - winning just one of their last six games in the Championship - the game in hand they possess over all of the sides that are jostling for a play-off spot means that a victory against United would put them back into contention.
Their biggest strength has arguably been their defensive record which only four sides, including Burnley have bettered so far this term.
That strength in defence will surely mean that Leeds will be relying on doing something they were unable to do against the Clarets and that's take the clear-cut opportunities that present themselves if they hope to back up another impressive performance with some points.