HITC Sport understands the ex-Gibraltar boss is looking to get into club management.
Bula was in charge of the tiny outpost as he guided them into the international arena for the first tie back in 2013, before he parted company with them earlier this year.
He has been linked with other national team jobs around the world, as well as some sporting director roles, but he is understood to have the ambition to move into club management, and now the Torquay job has sparked his interest.
The Gulls, who were relegated out of League Two in 2014, failed to bounce back into the Football League at the first time of asking last term and have now parted company with manager Paul Cox.
Despite their struggles both on and off the field, Bula is seemingly keen to land the role.
His representative Gregg Houghton confirmed to HITC Sport that he had applied for the role, adding: "Allen is keen on role, and he has applied, we will see how things go from here."