The striker, who was top scorer in Serie A in the 2013-14 campaign with 22 goals, has long been linked with a summer switch to Signal Iduna Park, with Jurgen Klopp claiming earlier this week that he would do "everything possible" to sign the 24-year-old.
A move for the Italy international - who is part of Cesare Prandelli's provisional World Cup squad - has always been complicated by the fact he is co-owned by Serie A champions Juventus.
However, reports emerged late on Thursday in Italy that both Juve and Torino - for whom Immobile was so impressive last season - had reached an agreement over ownership rights and had subsequently finalised a deal to sell the striker to Dortmund for a fee of around €19 million.
Zorc was not willing to confirm that a transfer had been agreed, but he did confirm to Kicker that there had been "good talks" held between the parties concerned.
Immobile left Torino officials disgruntled earlier in the spring when he admitted publicly that he would be interested in a move to the 2012 Bundesliga champions in order to secure Champions League football, though the Serie A outfit have always been adamant they wish to keep him.
Dortmund are in the market for offensive reinforcements after seeing Robert Lewandowski sign for rivals Bayern Munich and have already reached an agreement to sign Adrian Ramos from Hertha this summer.