A 'judgement' was apparently read out by militants before the man was thrown from the building as punishment for his sexuality, The Mirror has reported.
The man's reported death follows a number of public executions last month, including two men accused of homosexual acts who were also reportedly thrown off a building.
A series of photographs were released attributed to the "Information Office of the mandate of Nineveh", a city in Iraq.
The images claimed to show Isis militants carrying out "hudud", the system of fixed punishments for what the group's courts regard as serious crimes.
The pictures appear to show the men at the top of a large tower overlooking the city. One image showed a man falling towards the ground, while later images show both men's bodies at the base of the towers.
In December, Isis released a copy of its penal code, which listed so-called "crimes" punishable by amputation, stoning and crucifixion.
Some of the crimes included homosexuality and "spying for the unbelievers", both of which were deemed punishable by death.
- Independent