The Hoops are said to be among several clubs who are looking to sign the German u-21 international.
Dorsch currently plies his trade in the Bundesliga 2 for Heidenheim.
Dorsch is seen as a significant talent, but Heidenheim cannot demand an exorbitant fee for him as the midfielder has a buyout clause in his contract. Celtic, therefore, can sign him for a fee of £3.2m.
The defensive midfielder had joined Bayern Munich when he was 14 in 2012. He went on to develop from there but only made one senior appearance for the Bundesliga heavyweights.
However, it was a memorable one as he got himself on the scoresheet against Eintracht Frankfurt.