Assalaamu alaykum. Is it an innovation to say the Talbiyah as Thikr (expressions of remembrance of Allaah) and rememberance of Allaah on any average day? Can we say it like we say Alhumdulillaah (praise be to Allaah) and Subhaan Allaah (glory to Allaah)? Thank you.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

It is permissible for a person who is not in a state of Ihraam (ritual state of consecration) to say the Talbiyah; there is nothing wrong with it and it is not a Bid'ah (dispraised innovation).

Therefore, it is permissible for a person who is not in a state of Ihraam to repeat the Talbiyah, though saying the Tasbeeh (Subhaan Allah) and the like is better.

Ibn Taymiyyah said:

“There is nothing wrong for a person who is not in a state of Ihraam to say the Talbiyah, and he does not become in a state of Ihraam by saying it unless he had intended it (to enter the state of Ihraam). (Imaam) Ahmad said – in the narration of Al-Athram – 'A man may say the Talbiyah, but he does not become in a state of Ihraam and is not required to do anything, as it was reported that Ibraaheem said, '‘Abdullah (ibn Mas'ood) came back from his village near Qaadisiyyah, and he found some people saying the Talbiyah at An-Najaf, so they aroused his longing (to visit the Ka’bah), and he said, 'Labbayka the number of dust, Labbayka.''” [narrated by Sa'eed]

It was also reported from 'Ataa'  Al-Hasan, and Ibraaheem, that they did not see any harm for a person who is not in a state of Ihraam to say the Talbiyah that a man knows; this is because the Prophet used to say in the supplication of opening the prayer, “Labbayka wa sa’dayka, wal-khayru fi yadayka, wash-sharru laysa ilayka, ana minka wa ilayka (Here I am, happy to serve You. All good is in Your Hands, and evil is not from You. I exist by Your will and belong to You).” [Muslim]

Allah knows best.