There is nothing confirmed from the Prophet, upon whom be peace, regarding supplications during ablution save the hadith of Abu Musa al-Ash’ari who said, “I came to the Messenger of Allah with water. While he was performing ablution, I heard him supplicate, ‘O Allah, forgive my sins. Make my residence spacious for me and bless me in my provisions.’ I said, ‘O Prophet of Allah, I heard you supplicating such and such.’ He said, ‘Did I leave anything out?” (Related by an-Nasa’i and Ibn as-Sunni with a sahih chain.) An-Nawawi includes this event under the chapter, What is to be said after one completes the ablution, and Ibn as-Sunni has it under, What is to be said when one is in the state of ablution.
An-Nawawi holds that both meanings may be implied from the hadith.