The Baggies have had to wait patiently for the 23-year-old to resolve a contract dispute with Dutch Eredivisie club Heracles Almelo.
Davidson, who played in Australia's three World Cup group matches, believed he had finished his contract with Heracles and had become a free agent.
Heracles, however, informed Davidson they had triggered a one-year option on that deal and he was still their player.
Albion have played their part in the row, and now talks over terms and a medical are scheduled to go ahead this week.
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