According to the vast majority of scholars and imams, offering a sacrificial animal on `Eid Al-Adha by non-pilgrims is not considered as obligatory but only sunnah mu’akkadah (highly recommended act).
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: As far as sacrifice of animals on `Eid Al-Adha with respect to non-pilgrims is concerned, according to the vast majority of scholars and imams, it is not considered as obligatory but only sunnah mu’akkadah (highly recommended act).
Imam Abu Hanifah, however, adopted the position that sacrifice is obligatory upon those who can afford to do it. All other scholars and jurists, including the Prophet’s Companions, successors and others, do not consider sacrifice as obligatory but as a strongly recommended Sunnah.
Imam Muslim reported on the authority of Umm Salamah that the Prophet (peace and blessings be upon him) said, “When the ten days of Dhul-Hijjah enters, if anyone wishes to sacrifice, he shall not remove his hair or nails (until the sacrifice is done).” Imam Ash-Shafi`i comments on this saying, “It is clear from the phrase, ‘if anyone wishes to sacrifice’ that sacrifice is only recommended and not obligatory on everyone.”
Imam Ahmad and Ibn Majah reported that the Prophet (peace and blessings be upon him) said when asked about the significance of sacrifice, “It is a sunnah of your ancestor Ibrahim (upon whom be peace).”
Coming to the issue of the status of sacrifice in the case of pilgrims, it all depends on the form of Hajj they are performing. If they are performing ifrad (Hajj alone), then sacrifice is not obligatory. If, on the other hand, they are performing either tamattu` or qiran (Hajj and `Umrah), then sacrifice is obligatory on them.