It is Sunnah to say the takbeer out loud and to recite Qur’aan out loud in a prayer in which Qur'aan is to be recited out loud, but it is not obligatory, so if a person says them quietly there is nothing wrong with that and his prayer is valid.
But you have to move the tongue and form the words, and they cannot be uttered without doing that, whether in a prayer in which Qur’aan is to be recited out loud or one in which it is to be recited quietly.
Some fuqaha’ stipulated that the worshipper should be able to hear his own voice, but the correct view is that it is sufficient to move the tongue and form the words.
The details of that opinion are as follows:
1 – The majority of Shaafa’i and Hanbali scholars, and Hanafi scholars according to the more correct of their two views, are of the opinion that it is obligatory for the worshipper to utter the takbeer in such a way that he can hear his own voice, and it is not sufficient for him to move his tongue without making a sound. The same applies to all dhikr; it does not count if there is no sound.
2 – Some of the scholars are of the view that it is acceptable to move the tongue and form the words without making a sound. This is the view of the Maalikis and of the Hanafis according to the other report. It was also the view favoured by Shaykh al-Islam Ibn Taymiyah. Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (1/276): The worshipper must be able to hear himself [i.e., saying the takbeer] whether he is leading the prayer or otherwise, unless he has a problems, such as being deaf, or something is preventing him from hearing, in which case he should do it as if he could hear or as if there was no problem. Because dhikr is something that is to be done verbally, and there can be no speech without sound, and sound is what can be heard, and the closest of listeners to him is himself, so if he cannot hear it then he does not know whether he has said the word. There is no difference between men and women with regard to what we have said. End quote.
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (3/256):
The minimum form of reciting quietly is such that a person can hear himself if he is sound of hearing and there is no problem such as surrounding noise and the like. This is general in meaning and applies to recitation, takbeer, tasbeeh when bowing and so on, tashahhud, salaam and du’aa’, whether the prayer is obligatory or naafil; nothing of it counts unless he can hear himself, if he is sound of hearing and there is no problem. End quote.
See: Tabyeen al-Haqaa’iq (1/127) and al-Bahr al-Raa’iq (1/356).
Khaleel (may Allaah have mercy on him) said in his Mukhtasar: … and reciting al-Faatihah by moving the tongue is a must for the one who is leading the prayer and the one who is praying by himself, even if he cannot hear himself. End quote.
Al-Hattaab (may Allaah have mercy on him) said: Ibn Naaji said in Sharh al-Risaalah: It should be noted that the minimum form of reciting quietly is that one should move the tongue whilst reciting, and the maximum is when he can hear himself only. The minimum form of reciting out loud is when he can hear himself and those who are close to him can hear him, and the maximum is limitless. End quote. In Sharh al-Mudawwanah it adds: Whoever recites in his heart whilst praying is like one who does not recite at all. Hence it is permissible for one who is junub to recite in his heart. Ibn ‘Arafah said: Sahnoon ibn al-Qaasim heard that moving the tongue is acceptable for one who is reciting quietly, but it is better if he can hear himself. End quote from Mawaahib al-Jaleel (1/535).
Al-Mardaawi (may Allaah have mercy on him) said in al-Insaaf (2/44): The words “reciting as much as he can hear himself” mean that the worshipper must recite aloud in prayers where Qur’aan is recited quietly and say the takbeer and so on in such a way that he can hear himself. This is our view, and it is the view of our companions, and it was stated definitely by most of them. Shaykh Taqiy al-Deen [Ibn Taymiyah] favoured the view that it is sufficient to form the letters, even if he cannot hear himself, and he mentioned it as a view in his madhhab. I say: I favour this view. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) thought the view of the Maalikis and Shaykh al-Islam was more correct. He said:
With regard to the words “he says”, if we say that saying may be done with the tongue, is it essential that he can hear himself saying it? There is a difference of opinion among the scholars concerning this. Some of them say that there must be a sound that he can hear himself. This is the correct view; even if those who are next to him cannot hear him, he has to be able to hear himself. If he speaks without hearing himself, then there is no point in forming these words. But this view is weak. The correct view is that it is not essential that he be able to hear himself, because hearing is something extra to saying and speaking, and if something is extra to what is mentioned in the Sunnah, then the one who says that has to produce evidence for it. Based on that, if a person is certain that he has pronounced the words properly, but he did not hear himself, either because his hearing is weak or because of noise going on around him, or for some other reason, then the correct view is that all his words are acceptable and he does not have to do more than what is indicated by the texts, which is speaking. End quote from al-Sharh al-Mumti’ (3/25).
See also the answer to question no. 70577
Based on that, if you moved your tongue and lips in saying the takbeer, that is sufficient, but it is better if you say it in a voice that you can hear.
And Allaah knows best.