Stoger's contract at Westfalenstadion expires this summer, and an inconsistent second-half to the season has left Dortmund considering their options for next season.
Nice boss Lucien Favre is seen as a strong candidate to replace Stoger, but Goal understands that Villas-Boas has also been sounded out as a successor to Stoger.
Villas-Boas has not been involved in football since November, turning down a new contract at Shanghai SIPG to take a break from coaching and enter the Dakar Rally.
In January, he competed in the event, but was forced to retire from the competition after being taken to hospital when his Toyota Hilux crashed into a sand dune.
Following this success, Chelsea paid €15 million to buy him out of his Porto contract, but he was dismissed after just 40 games in charge of the Blues. He performed much better in his next job at Tottenham, but left by 'mutual consent' in December 2013 after some bad results in the Premier League.
Dortmund sporting director Michael Zorc has refused to give much away regarding Stoger's future at the club or who could replace him this summer, keeping his cards close to his chest any time the subject has been mentioned.
"We have always said that we take the time it takes to make the right decision," Zorc told Der Westen.
"When the time comes, we'll let you know. We are also very, very calm about this matter and do not let anyone influence us."