Concerns are growing over the talks with Sanchez, who is not close to signing a contract extension to his existing £130,000-a-week deal which is due to expire in 2018.
As a result, Arsene Wenger has identified Reus, who is valued at around £30m, as his contingency plan, should Sanchez leave the club.
Reus has just returned to the Dortmund team after a six-month injury lay-off, which caused him to miss out on Germany’s Euro 2016 squad.
According to The Sun, Wenger is a big fan of Reus and has tried to bring the 27-year-old to the Premier League in the past but Dortmund have managed to hold onto him, while Real Madrid have also admired him.
Sanchez is reportedly holding out for £200,000-a-week as well as the insertion of a buyout clause.
Arsenal have already agreed a contract extension for right-back Hector Bellerin and are confident they will keep Mesut Ozil with a new deal worth in the region of £200,000-a-week.
However, they are less certain about Sanchez’s future with Juventus and Manchester City – whose manager Pep Guardiola was in charge of him at Barcelona – both interested.