Sayyiduna Abu Hurayrah (may Allah be pleased with him) reports this saying of the Prophet (peace and blessings be upon him): "Indeed, Allah Almighty is al-Salam, so do not say anything before (His name). When 'As-salamu alaykum' is said, then say (in reply) 'As-salamu alaykum'."
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الأدب / 12755
In one narration, the words are: "When one of you intends (to greet), let him say 'As-salamu alaykum', for Allah Almighty is al-Salam, so do not begin with anything else before (the name of) Allah Almighty."
Abu Ya'la recorded it. Its chain contains a narrator, Abdullah bin Sa'id al-Maqburi, who is extremely da'if (weak). Some hadiths about the limit of the greeting of salam have already passed before this.
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الأدب / 12756