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The former Lions captain, who had a spell as co-manager with Keith Stevens six years ago, believes he has done enough to convince the board that he is the right man for the job, despite strong speculation that the club will appoint someone on the outside after David Tuttle's disasterous spell in charge.
Tuttle quite last month just days after taking Millwall down into League One and although The Lions' lost their last game away to Crewe 4-2, performances under McLeary have improved dramatically.
"I'd like to think I'll have a chance of being in charge," said McLeary. "But that's for them to decide and to sort out.
"I think early organisation will be of benefit to the club. It was a bit up in the air in terms of organisation at the start of this season."
McLeary's former charges, the Under-18 side, ended the year on a sour note, crashing 5-1 away to Ipswich Town.