Praise be to Allah.
The place for the intention is the heart, and speaking it out loud is bid’ah. It was not proven that the Prophet (peace and blessings of Allaah be upon him) or his companions spoke the intention for any act of worship out loud.
The Talbiyah in Hajj and ‘Umrah is not the intention.
Shaykh Ibn Baaz (may Allaah have mercy on him) said:
Speaking the intention is a bid’ah (innovation) and doing so loudly is even more sinful. Rather the Sunnah is to make one's intention in the heart, because Allaah knows that which is secret and what is even more hidden. Allaah says (interpretation of the meaning):
“Say: Will you inform Allaah of your religion while Allaah knows all that is in the heavens and all that is in the earth?”
It was not narrated from the Prophet (peace and blessings of Allaah be upon him) or the Sahaabah or any of the most prominent imams that they spoke the intention out loud. From this we may understand that it is not prescribed, rather it is an innovation that has been introduced into the religion. And Allaah is the Source of strength.
Fataawa Islamiyyah, 2/315
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:
It was not narrated that the Prophet (peace and blessings of Allaah be upon him) spoke the intention out loud, whether for prayer, wudoo’, fasting or any other act of worship. Even in Hajj and ‘Umrah he (peace and blessings of Allaah be upon him) did not say, when he wanted to do Hajj and ‘Umrah, “O Allaah, I intend to do so and so.” It is not narrated that he did that or that he told any of his companions to do that. The most that has been narrated concerning that is that Dubaa’ah bint al-Zubayr (may Allaah be pleased with her) asked him for advice, saying that she wanted to do Hajj but she was feeling unwell. The Prophet (peace and blessings of Allaah be upon him) said to her: “Do Hajj and put a condition saying, ‘I will exit ihraam at the place where You cause me to fall ill,’ because your condition is valid before Allaah.’” In this case it is acceptable to speak out loud because resolving to do Hajj is like a vow, and a vow is spoken out loud, because if a person intends to make a vow in his heart, that is not a vow and is not counted as a vow. Because Hajj is like a vow and must be completed once started, the Prophet (peace and blessings of Allaah be upon him) commanded Dubaa’ah to say her condition out loud and say, “If something prevents me from completing my Hajj, then the place of my exiting ihraam is the place where You cause me to be unable to proceed further.”
With regard to what is proven in the hadeeth, that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Jibreel came to me and said, ‘Pray in this blessed valley, and say, ‘Umrah fi Hijjah or ‘Umrah wa Hijjah [‘Umrah and Hajj],’” that does not mean that he was speaking the intention out loud, rather what it means is that he was mentioning the acts of worship in his Talbiyah. The Prophet (peace and blessings of Allaah be upon him) did not speak his intention out loud.
Fataawa Islamiyyah, 2/216
And Allaah knows best.