All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is an obligation for whoever performs Hajj Qiraan or Hajj Tamattu' to offer a sacrificial animal in Makkah but the one who performs Hajj Ifraad is not obliged to do so.
According to the view of the majority of the scholars slaughtering an Udh-hiyah (a sacrificial animal – usually a sheep) on the days of ‘Eed (for whoever is not in Hajj) is a confirmed Sunnah from the Prophet, sallallaahu ‘alayhi wa sallam, and not an obligation in principle. It is a recommended act for both a pilgrim and for a non-pilgrim.
Therefore, if a pilgrim wants to offer a sacrifice on the days of ‘Eed in addition to the Hady (sacrificial animal as a part of the Hajj rituals), then he can do so and he will be rewarded for doing so, Allaah willing. He has the choice to offer the Udh-hiyah either in his country or in Makkah.
However, some scholars are of the view that a pilgrim is not required to offer the Udh-hiyah (sacrifice of ‘Eed), and that the Sunnah for a pilgrim is only to offer a Hajj sacrifice (Hady).
Allaah Knows best.