The Bees have watched the defender for some time and tried to sign him in August when Gremio were looking for £13.5m.
The 20-year old has yet to be capped by Brazil at full international level and the move will be subject to a work permit.
Vanderson is strong going forward and good at taking set pieces.
Talks are continuing with Vanderson and his representatives but all parties are hopeful of concluding a deal for January, says the Daily Mail.
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