Leeds play Fulham in the fifth round of the FA Cup on Tuesday night, but they also have a relegation battle to contend with in the Premier League.
As such new Leeds manager Javi Gracia may be tempted to rest a few key players for the FA Cup clash, but Kilgallon would advise him against doing so.
Killgallon wants to see Leeds’ best team against Fulham and has confidence that Gracia is of the same line of thinking.
The ex-Leeds star believes that a Whites win against Fulham would be hugely morale-boosting and would have the Elland Road faithful dreaming of Wembley.
Speaking on BBC Radio Leeds, Killgallon said: “To me you go strong there and Javi’s come in, he will want to win as many games as possible.
“No manager is like, he’s not going to go, well we’ll leave this one almost.
“I think have a run at it, if Leeds beat Fulham all the Leeds fans start going, ‘tell you what we’re not far off Wembley’.
“It gets exciting doesn’t it.”
Gracia once guided Watford to the FA Cup final, in the 2018/19 season, and Leeds fans will be hoping their new manager leads them to Wembley too.