The comments come as President Barack Obama recently decided to send US special operations forces to northern Syria and intensify strikes in the region.
Specific ideas in the discussion include whether multiple confirmed intelligence sources should be handed over prior to US airstrikes being approved, and whether forces can ease coordination among its coalition, the senior official added.
While the White House and the departments of Defense and State are interested in the potential changes, no formal proposals or "immediate decisions expected," the official added.
The US-led coalition against the Daesh, also known as ISIL/The Islamic State, comprised of 65 nations has been fighting the terror group in Iraq since August 2014 and in Syria since September 2014, but without the request of the Syrian government or the approval of the UN Security Council.
The Islamic State, also known as Daesh in Arabic, is a designated terrorist organization that is outlawed in many countries, including in Russia.