Blues were keen to strengthen their midfield department and McLeish saw the experienced schemer as an ideal signing.
Murphy was highly impressive for the Cottagers' in their successful 2008/09 campaign, scoring five Premier League goals.
However, McLeish came to the conclusion that there was no chance manager Roy Hodgson would allow Murphy to leave.
"Danny was someone we considered," he confirmed to the Birmingham Mail. "Well, we thought about him had Fulham been willing to let him go.
"But why would they be willing to let one of their most influential players go? People talk about Barry's age, but Murphy's 32 and has been a big factor in that Fulham side's success."
Although McLeish has signed Barry Ferguson and retained Lee Bowyer he remains in the hunt for an additional midfielder.
The former Rangers boss has a wealth of experience in the middle of the park and now wants youth to compliment his options.
McLeish has been linked with a loan move for Aston Villa's Craig Gardner, however, a deal is yet to materialise.
"I am still looking for that younger player I can get into the midfield," he continued.
"Someone who is maybe inexperienced in terms of games played but is a real dynamic and energetic player and who also is quite adept with a football.
"I know that's not going to be easy and these players generally cost upwards of £4million, probably more.
"We are spreading the net far and wide and we will keep doing our diligence. Maybe it's not the time to rush into anything in that respect.
"And if I can see someone who I can persuade the board, say 'come on, we've got to go for this boy', then they just may well do it."