McFadden's knee ligament injury - which was operated on last night - has put him out of football for several months.
Beausejour, as a left winger, could be viewed as an ideal replacement to take over McFadden's mantle.
McLeish has used McFadden more often than not on the left, but had pencilled him in for more time at centre-forward before his misfortune.
"Jean's more of a direct winger," McLeish told the Birmingham Mail. "James is more inter-action, coming inside and making runs across the face and supporting strikers.
"But in saying that, I was impressed with James performance against Liverpool.
"I was intending on keeping him there, in the striking department. So there would have been room for two of them."