A hadith like this has been transmitted by Anas, but no mention has been made of Pilgrimage.
Sahih Muslim Book 6, Hadith 20
← Previous Hadith I heard Anas b. Malik say: We went out for Pilgrimage from Medina. The rest is the same.

Sahih Muslim Book 6, Hadith 19 Next Hadith → Salim b. 'Abdullah (b. 'Umar) reported on the authority of his father that Allah's Messenger (ﷺ) observed the prayer of a traveller, i. e. two rak'ahs in Mina, and other places; so did Abu Bakr and 'Umar, and 'Uthman too observed two rak'ahs at the beginning of his caliphate, but he then completed four.

Sahih Muslim Book 6, Hadith 21