Nineveh Plain Refugee Act of 2014 - Directs the Secretary of State to establish or use existing processes in Iraq, Saudi Arabia, Lebanon, Jordan, Kuwait, Turkey, and Syria through which a qualifying alien in such a country may apply and interview for refugee admission to the United States.

Considers such an alien to be a refugee of special humanitarian concern eligible for priority 2 processing under the refugee resettlement priority system.

Authorizes the Secretary to: (1) suspend in-country processes in such a foreign country for up to 90 days, and (2) extend a suspension upon congressional notification.

Directs the Secretary to establish one or more categories of aliens who are or were nationals or residents of a territory controlled by the group known as the Islamic State of Iraq and the Levant (ISIL), or any successor name, in Iraq, Saudi Arabia, Lebanon, Jordan, Kuwait, Turkey, or Syria, and who share common characteristics that identify them as targets of persecution in that country on account of race, religion, nationality, membership in a particular social group, or political opinion.

Provides that:

• an alien provided priority 2 processing shall not be counted against annual refugee admission limitations,
• no alien shall be denied the opportunity to apply for admission under this Act solely because such alien qualifies as an immediate relative or is eligible for any other immigrant classification,
• each denial for refugee status under this Act shall be in writing and shall state the reason for denial,
• each qualifying alien who after June 1, 2014, and before the date of enactment of this Act was denied refugee status shall be permitted to reapply for such status, and
• if the Secretary determines that an alien in such country who has applied for U.S. refugee admission pursuant to this Act is in imminent danger the Secretary shall make a reasonable effort to provide such alien with protection or the immediate removal from the country.