The Switzerland international has spent seven seasons with the Italian giants, winning the Scudetto in each campaign.
He has also won four Coppa Italia titles but he is set to leave the club this summer when his contract expires on June 30.
Lichtsteiner, 34, has made 26 appearances this season but reports claim he is now ready to play in Germany for the first time in his career.
He has spent the last 10 years in Italy but will be hoping to help Dortmund push on after Peter Stoger stepped down last week.
Bayer Leverkusen have signed keeper Lukas Hradecky from Eintracht Frankfurt ahead of Bernd Leno's likely exit.