Both the Greek-speaking Byzantines and the Tang dynasty sent diplomatic envoys to the Türk qaghanate in Central Asia. The Türks led by Ishtemi Qaghan first allied with the Byzantines in 568 against Sassanian Persia. After receiving an embassy of Türks and Sogdians, the Byzantine emperor Justin sent the general Zemarchus to Central Asia, where he met with Ishtemi to negotiate an alliance. Diplomatic relations between the Türks and the Byzantines persisted even after the Türk qaghanate splintered into the Western and Eastern Türks.

Likewise, there were Tang dynasty religion pilgrims, merchants, and diplomatic envoys traveling through Türkic territory. The Chinese Buddhist monk Xuanzang and Tang ambassadors visited the Western Türk ruler Ton Yabghu around the 620s. By 657, the Tang dynasty conquered the Western Türks and installed puppet rulers to control the territory as Tang protectorates.

While a specific event doesn't come to mind at the moment, it's not inconceivable that a Byzantine envoy may have encountered someone from the Tang dynasty in Central Asia.

For further reading, see Jonathan Karam Skaff, Sui-Tang China and Its Turko-Mongol Neighbors: Culture, Power and Connections, 580-800 (Oxford University Press, 2012).