The BVB target is co-owned by Juventus and their city rivals but the Granata do not want to lose their top scorer this summer
The German giants are looking to bolster their forward line ahead of Robert Lewandowski's exit this summer and have been widely linked with a move for the Italian.
Reports stated that BVB officials were in Turin for negotiations this week with both Juventus and Torino, who co-own the player, but Cairo wants to keep his star man.
"Torino own 50 per cent of Immobile, just as much as Juventus," he told reporters.
"So, if BVB want Immobile, they have to discuss it with us as well. I have no intention of selling Immobile.
"This operation started in a less than appropriate time for our club."
Torino face a crucial home game with Parma this weekend as they look to secure a Europa League place for next season.