The Birmingham Mail says Irvine hopes to complete the signing of Davidson - once the Baggies have established his contractual situation with Heracles Almelo.
Australia international Davidson is in England after failing to report for training with Dutch club Heracles.
The Eredivisie club maintain he is under contract with them, but the left-back disputes that.
Albion have been advised to sit tight while checks are made as to whether he is a free agent or if he has a 12-month tie-in with Heracles.
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