The Gunners were tipped to bring in the Portugal international ahead of the 2021-22 campaign, but nothing came of the speculation.
According to Italian outlet Gazzetta dello Sport, Arsenal were informed at the time that Lille were open to business.
However, the Ligue 1 side supposedly refused to budge on their €35m (£30m) valuation and a deal could not be struck.
Sanches has yet to score in eight league and Champions League appearances for Lille this term, though he did net for Portugal in their 2-1 loss to Serbia on Sunday.
AC Milan and Liverpool are rumoured to be weighing up a move for the 24-year-old in 2022. body check tags ::