Per talkSPORT, the Albion are hoping to secure Nelson in the summer for a cut price fee.
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While Nelson has always wanted to make it in the Arsenal first team, he is prepared to move to save his career.
The 24-year-old has not started a single Premier League game for the title chasers this season.
While his contract runs until 2027, the club may not object to cashing in on him.