Saka, 18, has impressed in his first season of professional football, with three goals and nine assists.
Sancho on the way out
Jadon Sancho could be set for a move away from Signal Iduna Park and to Manchester United in a transfer that would set the reds back around £100m, according to the same report.
The Bundesliga club have targeted the gunners' ace, Julian Favre's side once again turning to the English market to find young talent.
Saka is not the only young Englishman that BVB are interested in, however, and the NRW side are forerunners to sign Birmingham City youngster Jude Bellingham.
Bellingham has been in talks with multiple clubs around the world for deals reportedly worth over £30m, with Manchester United legend Sir Alex Ferguson giving the 16-year-old a tour around their Carrington training complex.
Saka to switch London for Dortmund
Despite currently being utilised as a left-back when playing in North-London, Saka could help to fill the role left by the departure of Jadon Sancho, providing extra support if Julian Draxler chooses to sign for BVB.
The youngster currently has just over twelve months left on his £7,000 a week contract.
Earlier this week, Football.London announced that no talks had taken place between the Gunners' hierarchy and Saka to look to renew his deal since February.
Last month, Arsenal manager Mikel Arteta gave some clarity on his contract situation, saying:
"The club is doing what it has to do and is having conversations.
"We'll get it resolved."
The Gunners are committed to keeping the 18-year-old at the Emirates, however, and would be prepared to offer him a significant pay rise.