Manchester United were found to be tracking Lyanco, 20, last month.
The Daily Mirror claimed United scouts were watching the Sao Paulo ace, with a mind to making a summer bid worth £10million.
But Torino have got there first, offering a lower fee for the centre-back that includes add-ons.
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That is according to Brazilian newspaper Goloboesporte, who claim the Serie A club are set to land Lyanco for £6.9m.
It is claimed £5.2m of that fee will be paid up front when Lyanco completes his switch to Italy in the summer transfer window. The rest will be topped up by performance-related clauses.
United recently appointed former Brazil chief scout Paulo Henrique Xavier as their new scout in the country – a move that they hope will secure them access to Brazil's best new talent.
Manchester United and Juventus were linked with Lyanco
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Brazil youth star Lyanco (left) is set to join Torino
Lyanco (right) played against England U20s last summer
Lyanco has impressed at Brazil youth level but is yet to make the step up to the full national side.
Juventus and Atletico Madrid were also interested in the defender, who started his youth career at Botafogo before switching allegiances two years ago.