When worshipping Allaah, the Muslim must worship Him in the manner that He has prescribed. The basic principle regarding acts of worship is tawqeef (i.e., acts of worship are to be based solely on Qur’aan and saheeh Sunnah with no room for personal opinion). No kind of act of worship is prescribed except with daleel (evidence from sharee’ah). Whoever comes up with something that was not prescribed by Allaah or His Messenger has introduced an innovation into the religion of Allaah, and this action of his is to be rejected, because in order for a deed to be acceptable (to Allaah), it must meet two conditions: 

1-       It must be sincerely for the sake of Allaah alone. Allaah says (interpretation of the meaning):

“And they were commanded not, but that they should worship Allaah, and worship none but Him Alone (abstaining from ascribing partners to Him)”[al-Bayyinah 98:5] 

2-       It should be according to the way of the Prophet (peace and blessings of Allaah be upon him) and the message he brought. Allaah says (interpretation of the meaning):

“And whatsoever the Messenger (Muhammad) gives you, take it; and whatsoever he forbids you, abstain (from it)”[al-Hashr 59:7] 

So it is not permissible to innovate any kind of act of worship that was not prescribed by the Prophet (peace and blessings of Allaah be upon him). The Prophet (peace and blessings of Allaah be upon him) said: “Whoever does an action that is not in accordance with this matter of ours (Islam) will have it rejected.” (Narrated by al-Bukhaari, 2697; Muslim, 1718). 

Al-Tirmidhi narrated from Imaam Ahmad ibn Hanbal from the hadeeth of al-‘Irbaad ibn Saariyah that the Prophet (peace and blessings of Allaah be upon him) said: “I urge you to adhere to my Sunnah and the way of the Rightly-Guided Khaleefahs. Adhere to it and bite onto it with your back teeth (i.e., cling firmly to it). And beware of newly-invented matters, for every newly-invented matter is an innovation and every innovation is a going-astray.” (Narrated by al-Tirmidhi, al-Sunnah, 3991. Al-Albaani said in Saheeh Sunan Abi Dawood, no. 3851, it is saheeh). So the Muslim should not go beyond that which the Prophet (peace and blessings of Allaah be upon him) brought and prescribed. 

The Sahaabah transmitted the description of the wudoo’ of the Prophet (peace and blessings of Allaah be upon him), and none of them transmitted this (the action mentioned in the question) from the Prophet (peace and blessings of Allaah be upon him), so we should follow that which he brought. 

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said concerning the matter of speaking the intention (niyyah) out loud:  

“It is not mustahabb to utter it out loud, because that is an innovation (bid’ah) that was not narrated from the Messenger of Allaah or from his companions, and the Prophet did not command anyone among his ummah to utter the intention out loud; he never taught that to anyone among the Muslims. If that had been prescribed, the Prophet and his companions would not have neglected to convey it, because the intention is something that the Muslims must deal with every day and every night. Rather speaking the intention out loud is indicative of a defect in reason and religious commitment.”(Majmoo’ al-Fataawa, vol. 22, p. 231) 

Elsewhere he said: 

“All the things that people have innovated such as speaking the intention (niyyah) out loud before saying ‘Allaahu akbar’, before reciting the Talbiyah, when purifying themselves and in all acts of worship, are all kinds of innovations which were not prescribed by the Messenger of Allaah (peace and blessings of Allaah be upon him). Everything that is innovated in prescribed acts of worship, such as doing extra things that were not prescribed by the Messenger of Allaah (peace and blessings of Allaah be upon him) is a form of bid’ah (innovation) because the Prophet (peace and blessings of Allaah be upon him) used to do those acts of worship without doing these extra things. So doing them and persisting in doing so is a form of innovation and misguidance.”  

(Majmoo’ al-Fataawa, vol. 22, p. 223) 

With regard to the dhikr which is said before or after wudoo’, please see the answer to question no. 2165 

So the Muslim should give up anything that was not brought by the Prophet (peace and blessings of Allaah be upon him), and keep away from innovations introduced into the religion, because following innovations implies imitating the People of the Book. And the Muslim should strive to learn about his religion so that he will not fall into bid’ah. And Allaah knows best.