بسم الله الرحمن الرحيم
Wudhu is necessary in order to touch the holy Quran. It is not lawful to touch the holy Quran if the wudhu broke. However, one may recite the holy Quran or read any dua without touching the holy Quran. Wudhu is not necessary to recite the holy Quran or dua.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.