The 21-year-old, who is a target for Derby County, submitted a second written document yesterday despite having a similar formal request rejected by Albion earlier this month.
The Baggies again moved quickly to turn down his request.
Thorne's fresh move came just hours after the Baggies turned down a similar transfer request from defender Craig Dawson, who is wanted by Burnley.
Derby have already had a £950,000 opening offer and a second bid, believed to be worth up to £1.5m, rejected by Albion, who have insisted they will not sell Thorne.
They have also told Burnley that Dawson, aged 24, is not for sale.
But neither the Rams nor the Clarets are expected to give up easily.
Thorne angered Baggies officials earlier this month with an outspoken interview in a national newspaper.
It it he claimed to feel unwanted at The Hawthorns and would refuse to return to be a substitute.
His actions are likely to harden chairman Jeremy Peace's approach to the situation.