The Belgium international has fallen out of favour at Anfield, not featuring in the Premier League since the 2-1 win at Burnley on New Year's Day.
Dortmund, meanwhile, are believed to be seeking an upgrade on their current first-choice custodian, Switzerland international Roman Burki, in their bid to rival an increasingly dominant Bayern Munich.
According to The Sun, Liverpool are happy to sanction Mignolet's departure and will quote BVB a £10m fee for the 30-year-old's services.
The report also claims that Stoke City were also interested in Mignolet, but their relegation from the Premier League has made them an unlikely destination for the former Sunderland stopper.
Mignolet has made 202 appearances for Liverpool in all competitions since his 2013 move from the Stadium of Light.