The young Portugal international is available from the Ligue Une champions, with interest arriving from across Europe.
Lille are prepared to sell - but at a starting price of €35m.
Last season, Sancho helped Lille win the Ligue Une title, playing 29 games, scoring once and producing four assists. He also participated in all four of Portugal's games at this summer's Euro 2020.
However, Arsenal manager Mikel Arteta stated after their preseason friendly defeat to Chelsea on Sunday that he wished to keep hold of the Switzerland international. Xhaka scored Arsenal's goal in the 2-1 loss.
- updated August 3
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