Hi Jeff and Filiberto,
The fight of the Chinese dragon ( Shen-Long) with the Chinese phoenix, or rather the Fenghuang (as rightly precised by Jeff ) was obviously a well established motif in different areas of central and western Asia. Below it is illustrated on two extant Safavid rugs from the sixteen and seventeen centuries. In a very densely knotted and "naturalistic" version.
Persian. Safavid period 45 silk, phoenix and dragon motif. Detail. XVI-XVII
Persian. Safavid period 31.2 The Mantes rug. Detail 2. XVI. 783X379.Louvre.Paris .jpeg
The Chinese origin is rather evident. One can quite safely assume that this motif migrated west following the Mongol onslaught and under the Ilkhanid rulers (mid-thirteenth to mid-fourteenth century). One can also suppose that a prestigious and powerful "animal" like the dragon would have been used as totem, tribal symbol by some of the mongol- and turk clans which took part to the attack (just as tigers, wolves, lions were used etc..)
Best regards
Pierre