The Blues centre-back, who is yet to play this season because of an ankle ligament injury, is expected to be available for first team selection either during the festive period or thereabouts, according to the Blues boss.
"Martin Taylor is at a good level of fitness now and should be ready for the festive season or just after," McLeish has said.
"He will be okay for a reserve-team game very soon and we will also look to organise one or two friendlies at the training ground for him."