It is narrated from al-Muttalib bin Abdullah bin Hantab (may Allah have mercy on him) that people differed about the recitation in Zuhr and Asr, so they came to Kharijah bin Zayd bin Thabit (may Allah have mercy on him), and he said: My father (Zayd bin Thabit (may Allah be pleased with him)) told me that the Messenger of Allah (peace and blessings be upon him) led us in the Zuhr and Asr prayers, and during the standing his blessed lips were moving. I can only understand that they were moving because of recitation. So we also do the same.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3062