Blues manager McLeish is to field a strong side in Wednesday night's Carling Cup quarter-final with local rivals Aston Villa at St Andrew's.
It represents a golden chance for City to reach the last four - given Villa's lengthy injury list - for the first time since they lost to Liverpool in the 2001 final. But McLeish knows winning the competition will count for little if Birmingham were also to be relegated.
He said: "The draw has been kind to us with four home games this season and we've got to try and take advantage again. We're now in the quarter-finals and we've got to look to try and go all the way.
"We know that on paper Villa would still be the stronger team although, at St Andrew's, I wouldn't back against Birmingham, against anyone. Against Villa I've got to play as strong a team as I can."
McLeish added: "It would be great to lift some silverware but the Premier League is our priority, our bread and butter. If we lifted the Carling Cup and were relegated, that would be a disaster."