Jabir bin Abdullah (may Allah be pleased with both of them) narrates that the Messenger of Allah (ﷺ) never mentioned Hajj or Umrah by name in his Talbiyah.
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 817
Hadith Takhrijاسناده ضعيف جدا ، لضعف شیخ الشافعي اخرجه البيهقي : 40/5 ۔ وفى المعرفة السنن والآثار له (2717)۔
It is narrated from Abdullah bin Umar (may Allah be pleased with them both) that the Talbiyah of the Messenger of Allah (ﷺ) was: O Allah! I am present, I am present, there is no partner for You, I am present, surely all praise and blessings are for You, and the kingdom is for You, there is no partner for You. Nafi’ said that Abdullah bin Umar (may Allah be pleased with them both) would add these words to it: I am present, I am present, and I comply with Your worship, and (all kinds of) goodness are in Your hands. (All kinds of) desire and action are towards You. (That is, for You.)
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 818
Hadith Takhrijاخرجه البخارى، الحج، باب التلبية (1549) ومسلم، الحج، باب التلبية وصفتها ووقتها (1184)۔
It is narrated from Jabir bin Abdullah (may Allah be pleased with them both) that the Messenger of Allah (ﷺ) recited this Talbiyah with Tawheed: "Here I am, O Allah! Here I am. Here I am, You have no partner, here I am. Surely all praise and blessings are for You, and sovereignty is for You alone, You have no partner."
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 819
Hadith Takhrijأخرجه مسلم الحج، باب حجة النبي صلی اللہ علیہ وسلم (1218)۔
It is narrated from Abu Huraira (may Allah be pleased with him) that he states: Among the words of Talbiyah of the Messenger of Allah (peace be upon him) were also these: "I am present, O True Deity, I am present."
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 820
Hadith Takhrijاخرجه النسائي، مناسك الحج، باب كيف التلبية (2753) وابن ماجة ، المناسك ، باب التلبية (2920) ۔ وصححه ابن خزيمة (2623) ۔ والحاكم : 1 / 449 ، 450 ووافقه الذهبي۔
It is narrated from Mujahid (may Allah have mercy on him) that he states: The Messenger of Allah (ﷺ) would express his Talbiyah as follows: “Here I am, O Allah! Here I am, here I am, You have no partner. Here I am, surely all praise and blessings are for You, and the kingdom is Yours, You have no partner.” He said this until one day, when the people were returning, it was as if these words pleased him, so he added these words to it: “Here I am, true life is the life of the Hereafter.” Ibn Jurayj said: In my opinion, this was the day of ‘Arafah.
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 821
Hadith Takhrijاسناده ضعيف لإرساله : اخرجه البيهقي : 455 ۔ وفى المعرفة السنن والآثار له (2813)۔
It is narrated from Abdullah bin Abi Salamah, who reports that Sa’d bin Abi Waqqas (may Allah be pleased with him) heard one of his nephews reciting the Talbiyah, and he was saying, “O Possessor of the steps!” So Sa’d (may Allah be pleased with him) said, “What steps? Indeed, He is the Possessor of the steps, but in the time of the Messenger of Allah (ﷺ), we did not recite the Talbiyah in this manner.”
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 822
Hadith Takhrijاسناده حسن اخرجه البيهقي : 5/ 45 ۔ وفى المعرفة السنن والآثار له (2814) ۔ واحمد: 1/ 172 - وابن ابی شيبة (13467)۔
It is narrated from Muhammad bin Abu Bakr Thaqafi that he asked Anas bin Malik (may Allah be pleased with him) while both of them were going from Mina to Arafat in the morning, "What would you people do on this day with the Messenger of Allah (ﷺ)?" Anas (may Allah be pleased with him) replied: "Some of us would be reciting Talbiyah and no one would object to him, and some would be saying Takbir and no one would object to him."
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 823
Hadith Takhrijأخرجه البخاري، الحج، باب التكبير ايام منى واذا غدا الى عرفة (970) ومسلم، الحج، باب التلبية والتكبير في الذهاب من منى الى عرفات ..... الخ (1285)۔