(CNN) -- An ISIS attack against the West is a question of timing -- "not of inevitably, not of intent," according to the former head of the CIA, retired Gen. Michael Hayden
Speaking to CNN's Jim Sciutto on "Fareed Zakaria GPS," Hayden said he expects ISIS to attempt an attack on targets in the United States or Europe.
"ISIS is a very powerful local organization, and probably a reasonably powerful regional terrorist organization," Hayden said. "But it's one that has global ambitions -- and it has the tools."
There's no clear consensus inside the intelligence community as to whether ISIS, which calls itself the Islamic State, is currently capable of striking the West.
That debate came to the forefront last week after the Sunni militant group beheaded American journalist James Foley in retaliation for the airstrikes -- an act that Michael Morell, the former deputy director of the CIA, called the group's "first terrorist attack against the United States," in an interview with CBS.
"It's expressed the intent," Hayden said. "There's no way more powerful way to express their street credentials among the jihadist community than a successful attack against the West."
The U.S. military has conducted targeted airstrikes in order to stop ISIS's progress in the region. The Obama administration initially said the strikes were carried out in order to protect U.S. personnel at the consulate in Irbil, Iraq, and prevent the genocide of the Yazidi people, a religious minority in the country.
That mission has appeared to have been broadened -- strikes continued to hit ISIS targets near Irbil and the Mosul Dam on Sunday, U.S. Central Command said in a news release. The majority of the strikes have been in support of Iraqi forces near the dam, which briefly fell under ISIS control.
Hayden said that American airstrikes inside Syria, in addition to those being conducted in Iraq, would make a difference in the fight against ISIS. Airstrikes in Iraq come at the request of that government; Syria, however, is in the midst of a civil war in which almost 200,000 people have been killed. The United States has called for its President, Bashar al-Assad, to step down.
"It's not just about defense; it's not just about keeping the right people off of aircraft," Hayden said. "It's about offense. It's about disabling ISIS. It's about making them more worried, more consumed with protecting their own survivability rather than yours or mine."