It is recommended by Durr al-Mukhtar, Maroqi that you should not engage in “worldy talk” while engaging in Wudu, if one could easily engage in “worldy talk” afterwards. The reason Durr al-Mukhtar, Maroqi made this recomemndation is three-fold:
1) Muhammad (ṣalla llāhu ʿalay-hi wa-sallam) and his companions (radhi Allahu anhum) used to do Wudu in silence, and only talked when there was a “genuine reason to talk”.
2) Wudu is also meant to be an act of worship, and as such, it is good for this worship to be done silently.
3) Scholars recommend that Muslims do Zikhr and supplicate while doing Wudu, as doing so would grant you great reward. Talking needlessly may distract you from doing Zikhr and supplication.
May Allah help us to implement this ruling when we do Wudu ourselves.
Source: Informational Poster at Masjid Ul’ Aala